Question

please help:
if In = (integral sign)x^n e^3x dx
show that In = x^n e^3^x/3 - n/3 In - 1
and hence evaluate (integral sign) x^3 e^3^x dx

Answer 1

i think this is a set up for parts

Answer 2

\[\int u dv =uv-\int vdu\] put \[u=x^n, du =nx^{n-1}dx, dv=e^{3x}dx,v=\frac{1}{3}e^{3x}\]