Question

integral of [x (tan^2 x)] dx

Answer 1

\[\int\limits_{0}^{\Pi/3} x \tan^2x dx\] that's the question.

Answer 2

try a trig identity (secx)^2-(tanx)^2 =1
so
\[\int\limits_{0}^{\pi/3} x(\sec^{2}x-1)dx\]

Answer 3

And??? How to continue with that?

Answer 4

break up the integral and you could try integration by parts

Answer 5

thanks.

Answer 6

\[\sec^{2} x = \frac{1}{cos^{2}x} \]
Also \[cos^{2}x = \frac{1+ cos 2x}{2}\]
and further break the integral up