Exercise
$\frac{\cot\left(\frac{x}{2}\right)}{2}-\frac{\tan\left(\frac{x}{2}\right)}{2}$
Derivative of this function
$\frac{d}{dx}\left(\frac{\cot\left(\frac{x}{2}\right)}{2}+\frac{-\tan\left(\frac{x}{2}\right)}{2}\right)=\frac{1}{2}\left(-\frac{1}{2}\csc\left(\frac{x}{2}\right)^2-\frac{1}{2}\sec\left(\frac{x}{2}\right)^2\right)$
See step-by-step solution
Integral of this function
$\int\left(\frac{\cot\left(\frac{x}{2}\right)}{2}+\frac{-\tan\left(\frac{x}{2}\right)}{2}\right)dx=\ln\left(\sin\left(\frac{x}{2}\right)\right)+\ln\left(\cos\left(\frac{x}{2}\right)\right)+C_0$
See step-by-step solution