# Integration by parts

1. Oct 10, 2007

### azatkgz

1. The problem statement, all variables and given/known data
$$\int x^7e^{-x^2}$$

3. The attempt at a solution
for $$u=x^2$$
$$\int \frac{u^3e^{-u}du}{2}=-\frac{u^3e^{-u}}{2}+\int \frac{3e^{-u}u^2du}{2}$$
$$=-\frac{u^3e^{-u}}{2}-\frac{u^2e^{-u}}{2}+\int 3e^{-u}udu$$
$$=-\frac{u^3e^{-u}}{2}-\frac{u^2e^{-u}}{2}-3e^{-u}u+\int 3e^{-u}du$$
$$=-\frac{u^3e^{-u}}{2}-\frac{u^2e^{-u}}{2}-3e^{-u}u-3e^{-u}$$

Last edited: Oct 10, 2007
2. Oct 10, 2007

### TD

Good, but you forgot the factor 3 in the second term (and the constant of integration).

3. Oct 10, 2007

Ok.thanks