So, what is the problem asking for? Integration by Parts for ∫(z^3e^z)dz

[narutoish]

Homework Statement

∫((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.

 

[PeroK]

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

 

[Adithyan]

Homework Statement

∫((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 Statement

∫((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.