Originally Posted by

**x3bnm** I want to find the integration of following integral:

$\displaystyle \int x^3.e^{x^2}\, dx$

So i apply integration by part:

$\displaystyle u.v - \int v \,du\,\,$

$\displaystyle

Let \,\, u = x^3, du = 3x^2\,\,

and \,\, dv = e^{x^2}, v = 2x.e^{x^2}

$

So now th result is:

$\displaystyle \int x^3.e^{x^2}\, dx = 2x^4.e^{x^2} - \int\,\,6x^3.e^{x^2}\,\, dx$

$\displaystyle 7\!\!\int x^3.e^{x^2}\, dx = 2x^4.e^{x^2}$

$\displaystyle \int x^3.e^{x^2}\, dx = \frac{2x^4.e^{x^2}}{7} + C$

Am i right? Because the answer to this problem is different back of the book.

Answer is $\displaystyle \frac{(x^2 -1).e^{x^2}}{2} + C$

The way i did it i can't find anything wrong with it. Can anyone kindly tell what

is wrong with my way of solving this problem?