Riemann integral on trigonometric functions I have to calculate Riemann integral of function $g:[0;\pi/4]\rightarrow\mathbb{R}$ (on interval $[0;\pi/4]$) given as $g(x)=\frac{\tan(x)}{(\cos(x)^2-4)}$. Function $g$ is continous on interval $[0;\pi/4]$ so it is enough to calculate $\int_0^{\frac{\pi}{4}}{\frac{\tan(x)}{(\cos(x)^2-4)}}$. How to do that?

substitue $u = cosx$, then you will have $du = -sinx dx$. Then you will have 1 in numerator and some polynomial in denominator, which can be fractionized as $u * (u - 2) * (u + 2)$. Then your going to separate it to partial fractions. Rest is simple integration... Don't forget to change integration limits.
