How can I use integration by parts to solve this indefinite integral?

[razorlead]

Homework Statement

Indefinite Integral (x^3)(e^x)

Homework Equations

The Attempt at a Solution

I know I need to substitute t=x^2

t^(3/2)e^sqrt(t)

U=e^sqrt(t)
du=e^sqrt(t) dt

dv=t^(3/2)
V= (5/2)t^(5/2)

Because it has an exponential function, I know I need to use the trick of running parts twice and then setting the two parts equal to each other, but I'm stuck.

Thanks for your help

Razorlead

 

[Mark44]

Homework Statement

Indefinite Integral (x^3)(e^x)

Homework Equations

The Attempt at a Solution

I know I need to substitute t=x^2

t^(3/2)e^sqrt(t)

U=e^sqrt(t)
du=e^sqrt(t) dt

dv=t^(3/2)
V= (5/2)t^(5/2)

Because it has an exponential function, I know I need to use the trick of running parts twice and then setting the two parts equal to each other, but I'm stuck.

No, that isn't it.
Let u = x³, dv = e^xdx
That will get you to an integral involving x² and e^x.

Do integration by parts again, with u = x² and dv = e^xdx. That will get you to an integral involving x and e².

Do you see where I'm going with this?

 

[Dick]

The substitution isn't helping. Go for parts first. Try dv=e^x*dx, u=x^3. If you've got that right it's made the problem easier. And, yes, I think you'll need to do it twice more before you get rid of the last integral.