How to solve for integral of 2e^(2x)sin(e^(2x))

let u = 2x
du = 2
dx = 1/2du

∫ (e^u)sin(e^u) x 1/2du
1/2 ∫ (e^u)sin(e^u)

Aaaaand now I'm stuck. XP Please help!

∫2e^(2x)sin(e^2x) dx

This is a basic u substitution problem...

u = e^2x

du = 2e^2x dx

∫ sin(u) du

Integrate like normal...

-cos(u) + C

Plug back in e^2x for u...

Final Answer:
-cos(e^2x) + C

http://www.wolframalpha.com/input/?i=integral+of+2e^%282x%29sin%28e^%282x%29%29

click show steps

Possible intermediate steps:
integral 2 e^(2 x) sin(e^(2 x)) dx
Factor out constants:
= 2 integral e^(2 x) sin(e^(2 x)) dx
For the integrand e^(2 x) sin(e^(2 x)), substitute u = 2 x and du = 2 dx:
= integral e^u sin(e^u) du
For the integrand e^u sin(e^u), substitute s = e^u and ds = e^u du:
= integral sin(s) ds
The integral of sin(s) is -cos(s):
= -cos(s)+constant
Substitute back for s = e^u:
= -cos(e^u)+constant
Substitute back for u = 2 x:
= -cos(e^(2 x))+constant

I think you will have better luck if you say u= e^2x then du=2e^2x dx and then your integral will just be
sin(u). Good luck.