# Homework Help: Integral OH YES!

1. May 9, 2005

### ziddy83

Ok, here is the integral i seem to be having some issues with. I know there's a very simple step im missing.

$$\int_{}^{} e^x \sin(\pi x) dx$$

i attempted to do this using by parts integration.

I tried u = $$\sin(\pi x)$$ so du= $$\pi \cos(\pi x) dx$$
so then dv= $$e^x dx$$ and v= $$e^x$$

after using $$uv- \int v du$$ I seem to be going in circles...can someone help?

2. May 9, 2005

### quasar987

Do integration by parts on $\int v du$. You'll end up with

$$\int_{}^{} e^x \sin(\pi x) dx = something - \int_{}^{} e^x \sin(\pi x) dx$$

Aaah.. add $\int_{}^{} e^x \sin(\pi x) dx$ on both sides. Divide by two. ta-dam.

3. May 9, 2005

### shmoe

Small warning, it won't look quite like you've described, the constant won't be two.

4. May 10, 2005

### quasar987

Oh right.. because of the pies!

5. May 10, 2005

### Galileo

There's a quick alternative way using complex exponentials.

Since
$$e^x \sin (\pi x)= \Im (e^{x+i\pi x})=\Im (e^{x(1+i\pi)})$$

$$\int e^{x(1+i\pi)} dx=\frac{e^{x(1+i\pi)}}{1+i\pi}=\frac{(1-i\pi)e^{x(1+i\pi)}}{1+\pi^2}$$

Now take the imaginary part.