HARD Integration by Parts - (x^3e^x^2/(1+x^2)^2dx)

[@wasimvillidad3000]

This is an example of "the reverse quotient rule". The clue is the squared factor in the denominator.

[@kimmyl2912]

Thank youuu I had such a hard time plugging the wrong things for u and dv

[@ChristGodinyouItrust]

You're welcome!

[@Everosa314z]

Thanks for this, holy moly

[@andikusnadi1979]

so much thank you.

[@faresberarma3349]

Continue please the simplification The final result is 1/2*(exp(x^2) /(1+x^2))

[@ChristGodinyouItrust]

Close, thats not true, the final answer is 1/2*(exp(x^2))(1-x^2)/(1+x^2) +C. So you're missing the detail in the numerator. And while factored, this answer is no more appealing than my final answer. Sorry, not being defensive.

[@ChristGodinyouItrust]

Thank you for watching and for commenting.

[@narendrangopalakrishnan3697]

Fares Berarma is correct AFAIK. Also, another approach is to substitute t=1+x^2, then the integral becomes (1/2e)Int d((1/t)exp(t)) = (1/2t)exp(t-1) + C, which yields the simplified answer of exp(x^2)/(2(1+x^2)) + C.

[@ChristGodinyouItrust]

Cheers!

[@manuel3537]

thanks

[@franklinmejia3919]

There is a shorter way to solve it?

[@ChristGodinyouItrust]

Not that I know of. See below!

[@nicogehren6566]

nice question

[@ChristGodinyouItrust]

Thanks a lot bro!