integration Xtan^2 2X?

Question

Integrate x multiply by (tan^2 2x)

Answer 1

♠ thus y(x)*dx = dx*x*(tan 2x)^2;
{by parts: u=x, du=dx;
dv=dx*(tan 2x)^2 = dx*(1 -(cos2x)^2) /(cos2x)^2 =
=dx /(cos2x)^2 –dx; v=0.5*tan(2x) –x;};
♣ thus Y(x) =
= 0.5*x*tan(2x) –x^2 - 0.5∫dx*tan(2x) +∫x*dx =
= 0.5*x*tan(2x) –x^2 + 0.25ln|cos(2x)| +0.5*x^2=
= C -0.5*x^2 + 0.5*x*tan(2x) + 0.25ln|cos(2x)|;

Answer 2

-x^2/2 + Log[Cos[2*x]]/4 + (x*Tan[2*x])/2

use the online integrator: http://integrals.wolfram.com