Given the integrals A and B, find A+B? A=Integral x*cos^2 xdx B = Integral x*sin^2x dx

We have the integrals A and B defined as A = Int[x*(cos x)^2
dx]

and B = Int[x*(sin x)^2 dx]

A +
B

=> Int[x*(cos x)^2 dx] + Int[x*(sin x)^2
dx]

=> Int[x*(cos x)^2 + x*(sin x)^2
dx]

=> Int[x*((cos x)^2 + (sin x)^2)
dx]

use the property that (sin x)^2 + (cos x)^2 =
1

=> Int[x dx]

=> x^2 / 2
+ C

The value of A + B = x^2/2 +
C