I'm totally lost, help would be appreciated.

[Daisydukes]

Evaluate the integral:

. . . . .\(\displaystyle \displaystyle{ \int_0^{\sqrt{\ln(\pi)\,}}\, 2xe^{x^2}\,\sin\left(e^{x^2}\right)\, dx }\)

Thanks in advance.

 

[Ishuda]

Evaluate the integral:

. . . . .\(\displaystyle \displaystyle{ \int_0^{\sqrt{\ln(\pi)\,}}\, 2xe^{x^2}\,\sin\left(e^{x^2}\right)\, dx }\)

Thanks in advance.

Are you in the same class as thesheepdog?
http://www.freemathhelp.com/forum/threads/89062-trig-logarithmic-integral

 

[noahdinho]

Do a u substitution. Set u=e^(x^2). Then du=2xe^(x^2) which you have in the integrand.

 

[lookagain]

Do a u substitution. Set u=e^(x^2). Then du=2xe^(x^2) which you have in the integrand.

If u = e^(x^2), then du = 2xe^(x^2)dx.

 

[HallsofIvy]

Is there a reason why you are not even trying to do these problems? With something like "\(\displaystyle sin(e^{x^2})\)" surely the substitution \(\displaystyle u= e^{x^2}\) would have occurred to you as something to try.