Use integration by parts to find integral of x^(2)e^(-5x) dx

u=x^2 & dv=e^(-5x)


du=2xdx & v=-(1/5)e^(-5x)

int.x^(2)e^(-5x) dx=-x^2(1/5)e^(-5x)

=-(1/5)e^(-5x) +(2/5)=xe^(-5x)dx+int(1/5)e^(-5x)2xdx

=-(1/5)e^(-5x) +(2/5){=-x(1/5)e^(-5x)+int.(1/5)e^(-5x)}

=-(1/5)e^(-5x) +(2/5){=-x(1/5)e^(-5x)+(1/5)int.(e^(-5x)…

=[-x^2/5-2x/25-2/125]e^(-5x)+C

You will have to use integration by parts twice to solve this.

Start with u = x^2 and dv = e^(-5x)dx

When you work the first integration out, you will have xe^(-5x) inside the integral
Do integration by parts again using u = x

That will lead you to the answer. Watch you signs!!!!