Efficient Methods for Finding the Integral of e^(2x)sin(e^x)

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I tried several ways to find this it's just making me confused.
Integral of e^(2x)sin(e^x)dx

I tried Integration by parts but i can't seem to find out the integral of sin(e^x).
 
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how about letting u = e^x... and you do know that e^(2x) = e^x * e^x so...
 
hm, thanks ill try that
 
Here's another hint, you will eventually need to use integration by parts.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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