Integration by parts
Integral(udv)=uv-integral(duv)
In this case we will make u=x and dv=8e^(8x) so du=1 and v=e^(8x)
Now integral(8xe^(8x)) => xe^(8x) - integral(e^(8x)) => xe^(8x) - e^(8x)/8 => (e^(8x))(x-1/8)
Final answer:
(E^(8x))(x-1/8) + some constant C
Hope I helped :)