Evaluate tanx(secx plus tanx)dx

Explanation:

Given that, 

x(x+x)dx=x(x-x)(x+x)(x-x)dx

=x.x-2x2x-2xdx

=(xx-(2x-1))dx, since 2x=1+2x

=xxdx-2xdx+dx

=x-x+x+c, where c is the integrating constant 

Final Answer:

Hence the value of the integral is, x(x+x)dx=x-x+x+c, where c is the integrating constant.