Can anyone help me find the integral from (pi/4) to 0 of x tan^2 x dx?

Answer 1

First, use the trig identity tan²(x) = sec²(x) - 1.

Then, for the integral of x sec²(x) use integration by parts, with
u = x , dv = sec²(x) dx . Doing this will require that you integrate tan(x); to do this, write tan(x) = sin(x)/cos(x) and use the substitution z = cos(x), dz = -sin(x) dx