# Trying Integration by parts

∫((z^3)(e^z ))dz

## Homework Equations

I just tried u dv - ∫v du

## 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.

Related Calculus and Beyond Homework Help News on Phys.org
PeroK
Homework Helper
Gold Member
You just have to keep going. Parts, parts and parts again!

∫((z^3)(e^z ))dz

## Homework Equations

I just tried u dv - ∫v du

## 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.
Integrate $∫(3e^{z} (z^{2})) dz$ with integration by parts till you get the term$∫e^{z}dz$

Ray Vickson
Homework Helper
Dearly Missed

∫((z^3)(e^z ))dz

## Homework Equations

I just tried u dv - ∫v du

## 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.
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.