How to integrate by substitution? [on hold] The Next CEO of Stack OverflowHow to integrate $int frac1sin^4(x)cos^4(x),mathrm dx$?How to integrate this fourier transform?Integrate using substitutionIntegrate without substitutionIntegral by parts instead of substitutionIntegrate $int frac ln xx^2$ by U-SubstitutionHow to integrate this integral?.could this integral be solved using substitution?How to integrate without trigonometric substitutionHow to integrate $int fracdxcosh x + sinh x + 2$
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multiple labels for a single equation
How to integrate by substitution? [on hold]
The Next CEO of Stack OverflowHow to integrate $int frac1sin^4(x)cos^4(x),mathrm dx$?How to integrate this fourier transform?Integrate using substitutionIntegrate without substitutionIntegral by parts instead of substitutionIntegrate $int frac ln xx^2$ by U-SubstitutionHow to integrate this integral?.could this integral be solved using substitution?How to integrate without trigonometric substitutionHow to integrate $int fracdxcosh x + sinh x + 2$
$begingroup$
I have a question on how to integrate this equation by substitution. I only know how to do it by parts.
$ int :x^2e^-x dx$
integration
edited 2 days ago
Will E.
123
asked 2 days ago
Master IrfanMaster Irfan
61
New contributor
Master Irfan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
put on hold as off-topic by RRL, Jyrki Lahtonen, Michael Rybkin, YiFan, Cesareo yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Jyrki Lahtonen, Michael Rybkin, YiFan, Cesareo
add a comment |
$begingroup$
I have a question on how to integrate this equation by substitution. I only know how to do it by parts.
$ int :x^2e^-x dx$
integration
edited 2 days ago
Will E.
123
asked 2 days ago
Master IrfanMaster Irfan
61
New contributor
Master Irfan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
put on hold as off-topic by RRL, Jyrki Lahtonen, Michael Rybkin, YiFan, Cesareo yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Jyrki Lahtonen, Michael Rybkin, YiFan, Cesareo
$begingroup$
I don't think you can do this by substitution? This is a very standard integration by parts problem
$endgroup$
– Don Thousand
2 days ago
1
$begingroup$
Why do you want to solve it by substitution, if you can use integration by parts? Actually integration by parts here is the way to get the solution.
$endgroup$
– Crostul
2 days ago
$begingroup$
The question given to us asked us to do it by substitution XD
$endgroup$
– Master Irfan
2 days ago
$begingroup$
It can be solved by integration by parts.
$endgroup$
– Dbchatto67
2 days ago
add a comment |
$begingroup$
I have a question on how to integrate this equation by substitution. I only know how to do it by parts.
$ int :x^2e^-x dx$
integration
edited 2 days ago
Will E.
123
asked 2 days ago
Master IrfanMaster Irfan
61
New contributor
Master Irfan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I have a question on how to integrate this equation by substitution. I only know how to do it by parts.
$ int :x^2e^-x dx$
integration
integration
edited 2 days ago
Will E.
123
asked 2 days ago
Master IrfanMaster Irfan
61
New contributor
Master Irfan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Will E.
123
asked 2 days ago
Master IrfanMaster Irfan
61
New contributor
Master Irfan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Will E.
123
edited 2 days ago
Will E.
123
edited 2 days ago
Will E.
123
123
asked 2 days ago
Master IrfanMaster Irfan
61
New contributor
Master Irfan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Master IrfanMaster Irfan
61
asked 2 days ago
Master IrfanMaster Irfan
61
61
New contributor
Master Irfan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Master Irfan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Master Irfan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by RRL, Jyrki Lahtonen, Michael Rybkin, YiFan, Cesareo yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Jyrki Lahtonen, Michael Rybkin, YiFan, Cesareo
put on hold as off-topic by RRL, Jyrki Lahtonen, Michael Rybkin, YiFan, Cesareo yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Jyrki Lahtonen, Michael Rybkin, YiFan, Cesareo
$begingroup$
I don't think you can do this by substitution? This is a very standard integration by parts problem
$endgroup$
– Don Thousand
2 days ago
1
$begingroup$
Why do you want to solve it by substitution, if you can use integration by parts? Actually integration by parts here is the way to get the solution.
$endgroup$
– Crostul
2 days ago
$begingroup$
The question given to us asked us to do it by substitution XD
$endgroup$
– Master Irfan
2 days ago
$begingroup$
It can be solved by integration by parts.
$endgroup$
– Dbchatto67
2 days ago
add a comment |
$begingroup$
I don't think you can do this by substitution? This is a very standard integration by parts problem
$endgroup$
– Don Thousand
2 days ago
1
$begingroup$
Why do you want to solve it by substitution, if you can use integration by parts? Actually integration by parts here is the way to get the solution.
$endgroup$
– Crostul
2 days ago
$begingroup$
The question given to us asked us to do it by substitution XD
$endgroup$
– Master Irfan
2 days ago
$begingroup$
It can be solved by integration by parts.
$endgroup$
– Dbchatto67
2 days ago
$begingroup$
I don't think you can do this by substitution? This is a very standard integration by parts problem
$endgroup$
– Don Thousand
2 days ago
$begingroup$
I don't think you can do this by substitution? This is a very standard integration by parts problem
$endgroup$
– Don Thousand
2 days ago
1
1
$begingroup$
Why do you want to solve it by substitution, if you can use integration by parts? Actually integration by parts here is the way to get the solution.
$endgroup$
– Crostul
2 days ago
$begingroup$
Why do you want to solve it by substitution, if you can use integration by parts? Actually integration by parts here is the way to get the solution.
$endgroup$
– Crostul
2 days ago
$begingroup$
The question given to us asked us to do it by substitution XD
$endgroup$
– Master Irfan
2 days ago
$begingroup$
The question given to us asked us to do it by substitution XD
$endgroup$
– Master Irfan
2 days ago
$begingroup$
It can be solved by integration by parts.
$endgroup$
– Dbchatto67
2 days ago
$begingroup$
It can be solved by integration by parts.
$endgroup$
– Dbchatto67
2 days ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Though you would still need to do integration by parts in the end this is the best answer according to me you can get:
Taking $ x= ln (t), t=e^x $
$$ int (ln(t)) ^2 e^(ln t)^-1 dx $$
$$ int frac (ln(t)) ^2t dx $$
Now
$$ dx= frac1t dt $$
$$ therefore int ( ln (t) )^2dt $$
Integrating by parts:
$$ int ( ln (t) )^2dt = t(( ln t)^2-2(ln t)+2)+C$$
$$ therefore int (x) ^2 e^-x dx=e^x((x)^2-2(x)+2)+C $$
Hope this helps
answered 2 days ago
Rithik KapoorRithik Kapoor
31010
$endgroup$
add a comment |
$begingroup$
You can also do it by $u$-substitution.
Let $u= e^-t$; this means, $du = -e^-t dt$.
Then put these values in the original integral.
Solve the integral.
Put back the value of $t$ in place of $u$.
edited 2 days ago
Marvin Cohen
174117
answered 2 days ago
user50374user50374
11
New contributor
user50374 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
This makes the integral into $int -(log u)^2,du$ that's not simpler.
$endgroup$
– egreg
2 days ago
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Though you would still need to do integration by parts in the end this is the best answer according to me you can get:
Taking $ x= ln (t), t=e^x $
$$ int (ln(t)) ^2 e^(ln t)^-1 dx $$
$$ int frac (ln(t)) ^2t dx $$
Now
$$ dx= frac1t dt $$
$$ therefore int ( ln (t) )^2dt $$
Integrating by parts:
$$ int ( ln (t) )^2dt = t(( ln t)^2-2(ln t)+2)+C$$
$$ therefore int (x) ^2 e^-x dx=e^x((x)^2-2(x)+2)+C $$
Hope this helps
answered 2 days ago
Rithik KapoorRithik Kapoor
31010
$endgroup$
add a comment |
$begingroup$
Though you would still need to do integration by parts in the end this is the best answer according to me you can get:
Taking $ x= ln (t), t=e^x $
$$ int (ln(t)) ^2 e^(ln t)^-1 dx $$
$$ int frac (ln(t)) ^2t dx $$
Now
$$ dx= frac1t dt $$
$$ therefore int ( ln (t) )^2dt $$
Integrating by parts:
$$ int ( ln (t) )^2dt = t(( ln t)^2-2(ln t)+2)+C$$
$$ therefore int (x) ^2 e^-x dx=e^x((x)^2-2(x)+2)+C $$
Hope this helps
answered 2 days ago
Rithik KapoorRithik Kapoor
31010
$endgroup$
add a comment |
$begingroup$
Though you would still need to do integration by parts in the end this is the best answer according to me you can get:
Taking $ x= ln (t), t=e^x $
$$ int (ln(t)) ^2 e^(ln t)^-1 dx $$
$$ int frac (ln(t)) ^2t dx $$
Now
$$ dx= frac1t dt $$
$$ therefore int ( ln (t) )^2dt $$
Integrating by parts:
$$ int ( ln (t) )^2dt = t(( ln t)^2-2(ln t)+2)+C$$
$$ therefore int (x) ^2 e^-x dx=e^x((x)^2-2(x)+2)+C $$
Hope this helps
answered 2 days ago
Rithik KapoorRithik Kapoor
31010
$endgroup$
Though you would still need to do integration by parts in the end this is the best answer according to me you can get:
Taking $ x= ln (t), t=e^x $
$$ int (ln(t)) ^2 e^(ln t)^-1 dx $$
$$ int frac (ln(t)) ^2t dx $$
Now
$$ dx= frac1t dt $$
$$ therefore int ( ln (t) )^2dt $$
Integrating by parts:
$$ int ( ln (t) )^2dt = t(( ln t)^2-2(ln t)+2)+C$$
$$ therefore int (x) ^2 e^-x dx=e^x((x)^2-2(x)+2)+C $$
Hope this helps
answered 2 days ago
Rithik KapoorRithik Kapoor
31010
edited 2 days ago
answered 2 days ago
Rithik KapoorRithik Kapoor
31010
answered 2 days ago
Rithik KapoorRithik Kapoor
31010
answered 2 days ago
Rithik KapoorRithik Kapoor
31010
31010
add a comment |
add a comment |
$begingroup$
You can also do it by $u$-substitution.
Let $u= e^-t$; this means, $du = -e^-t dt$.
Then put these values in the original integral.
Solve the integral.
Put back the value of $t$ in place of $u$.
edited 2 days ago
Marvin Cohen
174117
answered 2 days ago
user50374user50374
11
New contributor
user50374 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
This makes the integral into $int -(log u)^2,du$ that's not simpler.
$endgroup$
– egreg
2 days ago
add a comment |
$begingroup$
You can also do it by $u$-substitution.
Let $u= e^-t$; this means, $du = -e^-t dt$.
Then put these values in the original integral.
Solve the integral.
Put back the value of $t$ in place of $u$.
edited 2 days ago
Marvin Cohen
174117
answered 2 days ago
user50374user50374
11
New contributor
user50374 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
This makes the integral into $int -(log u)^2,du$ that's not simpler.
$endgroup$
– egreg
2 days ago
add a comment |
$begingroup$
You can also do it by $u$-substitution.
Let $u= e^-t$; this means, $du = -e^-t dt$.
Then put these values in the original integral.
Solve the integral.
Put back the value of $t$ in place of $u$.
edited 2 days ago
Marvin Cohen
174117
answered 2 days ago
user50374user50374
11
New contributor
user50374 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
You can also do it by $u$-substitution.
Let $u= e^-t$; this means, $du = -e^-t dt$.
Then put these values in the original integral.
Solve the integral.
Put back the value of $t$ in place of $u$.
edited 2 days ago
Marvin Cohen
174117
answered 2 days ago
user50374user50374
11
New contributor
user50374 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Marvin Cohen
174117
edited 2 days ago
Marvin Cohen
174117
edited 2 days ago
Marvin Cohen
174117
174117
answered 2 days ago
user50374user50374
11
New contributor
user50374 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 days ago
user50374user50374
11
answered 2 days ago
user50374user50374
11
11
New contributor
user50374 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user50374 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user50374 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
This makes the integral into $int -(log u)^2,du$ that's not simpler.
$endgroup$
– egreg
2 days ago
add a comment |
$begingroup$
This makes the integral into $int -(log u)^2,du$ that's not simpler.
$endgroup$
– egreg
2 days ago
$begingroup$
This makes the integral into $int -(log u)^2,du$ that's not simpler.
$endgroup$
– egreg
2 days ago
$begingroup$
This makes the integral into $int -(log u)^2,du$ that's not simpler.
$endgroup$
– egreg
2 days ago
add a comment |
$begingroup$
I don't think you can do this by substitution? This is a very standard integration by parts problem
$endgroup$
– Don Thousand
2 days ago
1
$begingroup$
Why do you want to solve it by substitution, if you can use integration by parts? Actually integration by parts here is the way to get the solution.
$endgroup$
– Crostul
2 days ago
$begingroup$
The question given to us asked us to do it by substitution XD
$endgroup$
– Master Irfan
2 days ago
$begingroup$
It can be solved by integration by parts.
$endgroup$
– Dbchatto67
2 days ago