# Math Help - integration by parts help

1. ## integration by parts help

im currently trying to integrate:

x²e^(x^3) dx

u = x² dv = e^(x^3)
du = 2dx v = e^(x^3)

and now using integration by parts formula i get

= ( x² )( e^( x^3 ) ) - integrate[e^(x^3)2xdx]

im a lil baffled on what to do next because i still cant integrate the bolded section! thx

2. You dont need by parts here..

just use substitution rule and let $u=x^3$

3. You don't use integration by parts for this integral, you use substitution.

$\displaystyle \int{x^2e^{x^3}\,dx} = \frac{1}{3}\int{3x^2e^{x^3}\,dx}$

Let $\displaystyle u = x^3$ so that $\displaystyle \frac{du}{dx} = 3x^2$ and the integral becomes

$\displaystyle \frac{1}{3}\int{e^u\,\frac{du}{dx}\,dx}$

$\displaystyle = \frac{1}{3}\int{e^u\,du}$

$\displaystyle = \frac{1}{3}e^u + C$

$\displaystyle = \frac{1}{3}e^{x^3} + C$.

4. Originally Posted by maybnxtseasn
im currently trying to integrate:

x²e^(x^3) dx

u = x² dv = e^(x^3)
du = 2dx v = e^(x^3)
Where did you get the idea that $\displaystyle \int e^{x^3}~dx = e^{x^3}$ ? The value of this integral is...complicated.

-Dan