# Trying Integration by parts

1. Feb 4, 2014

### narutoish

1. The problem statement, all variables and given/known data
∫((z^3)(e^z ))dz

2. Relevant equations

I just tried u dv - ∫v du

3. The attempt at a solution

u = z^3 dv = e^z
du = 3z^2 v = e^z

= z^3e^z - ∫(3e^z (z^2)) dz

I got this far but after that if I try integration by parts again, it gets too confusing.

2. Feb 4, 2014

### PeroK

You just have to keep going. Parts, parts and parts again!

3. Feb 4, 2014

Integrate $∫(3e^{z} (z^{2})) dz$ with integration by parts till you get the term$∫e^{z}dz$
You can avoid confusion by using some extra symbols. Let $I = \int z^3 e^z \, dz$. Integration by parts gives you $I = z^3 e^z - 3I_1$, where $I_1 = \int z^2 e^z \, dz$. Now look at $I_1$ in the same way, etc. Using separate symbols like that helps to keep things straight and to reduce errors.