# Thread: S x ( e ^ [SQRT[X]] - e ^ -3 * x^2) * dx

1. ## S x ( e ^ [SQRT[X]] - e ^ -3 * x^2) * dx

Here is my problem:
S x ( e ^ [SQRT[X]] - e ^ -3 * x^2) * dx . I have tried to call all my friends, but no one knew :/

2. You made the right thing when you split the integral into two.

Alright,

$\int xe^{x^2}dx=\frac{e^{x^2}}{2}+C$

Now to the first integral:

$\int{xe^{\sqrt{x}}dx$

First... substitute $\sqrt{x}=t$ and you will get:

$2\int {e^t}{ t^3}dt$

Now you can do integration by part 3 times... or:

Find the coefficients of:

$\int {e^t}{ t^3}dt=Ae^t {t^3}+Be^t {t^2}+Ce^t {t}+De^t$

(by differentiation)