Question

How to solve this?\[\int xe^{6x}dx \]

Answer 1

Let u = x
dv = e^(6x) dx
v = e^(6x)/6
du = dx
uv - ∫v du
x*e^(6x)/6 - ∫e^(6x)/6 dx eval. from 0 to 1
x*e^(6x)/6 - e^(6x)/36 eval. from 0 to 1
= e^(6)/6 - e^(6)/36 + 1/36
= (5*e^6 + 1)/36