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