Hello,

Please find the solution:

We are to evaluate, ∫x(x+4)12⋅dx .

We shall accomplish this by substitution.

Let, (x+4)=t
⇒dx=dt (By simple differentiation).

Thus, the integral becomes,

∫x(x+4)12⋅dx=∫t−4t12⋅dt

=∫t12⋅dt−∫4t−12⋅dt

=23t32−8t12+C , where C is the integration constant.

In terms of x , the integral may be now written as,

∫x(x+4)12⋅dx=23(x+4)32−8(x+4)12+C

Hope this helps, Good Luck.