Problem with solving the integral of the Gaussisin function

[M P]

Greetings ...
Please help me to solve this problem.
If we know that

and we intend to solve the following integral by parts:


We will have:
View attachment 18813



And my answer is wrong.
Please help me.
thanks...

 

[Steven G]

Your integral of v is not correct. I would choose u = x, instead of u = x^2.

See what you can do with that and please post back with your results.

 

[M P]

Your integral of v is not correct. I would choose u = x, instead of u = x^2.

See what you can do with that and please post back with your results.

Thanks ^ +Infinity
Unfortunately, I always thought:
That I was always wrong.

and true answer is:




Thank you again.
I wish you victory and success...
With respect

 

[HallsofIvy]

This is very strange! You start by saying
"If you know that \(\displaystyle \int_0^\infty e^{-ax^2}dx= \frac{\sqrt{\pi}}{2\sqrt{a}}\)"
but don't use it! Instead you later assert that
\(\displaystyle v= \int e^{-ax^2}dx= \frac{1}{-2ax}e^{-ax^2}\).
With that "x" in the denominator, that can't even be evaluated at x= 0!

Your basic error is that you are trying to treat "x" as if it were a constant.