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November 11th, 2017, 09:42 AM   #1
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Integral problem

Hello people!

I was given the following problem:

"Find the integral of (x^2+1)*e^((x^2)/2)"

I already know the solution (x*e^((x^2)/2)), because [f(x)g(x)]'=f'(x)g(x) + f(x)g'(x) where f(x)=e^((x^2)/2) and g(x)=x.

But I was wondering if there is a "nice" method that leads to solution. I tried integrating by parts and some substitutions but I was unable to find the solution that way.

Thanks for reading and have a nice day.
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November 11th, 2017, 10:20 AM   #2
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Originally Posted by Strom159 View Post
Hello people!

I was given the following problem:

"Find the integral of (x^2+1)*e^((x^2)/2)"

I already know the solution (x*e^((x^2)/2)), because [f(x)g(x)]'=f'(x)g(x) + f(x)g'(x) where f(x)=e^((x^2)/2) and g(x)=x.

But I was wondering if there is a "nice" method that leads to solution. I tried integrating by parts and some substitutions but I was unable to find the solution that way.

Thanks for reading and have a nice day.
I don't think you are going to find one. It's easy to check backward but there is a term you would need to add and subtract from the initial expression and that term is rather ugly. You would probably have to have a real good knowledge of Calculus to even think about it. (I can recognize what's going on, but only in reverse.)

And you should stay far away from any advice Denis has.

-Dan
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