Question

первообразная
$\cot( \frac{x}{2} )$
ctg x/2​

Answer 1

Ответ:

$\displaystyle f(x)=ctg\dfrac{x}{2}\\\\F(x)=\int ctg\frac{x}{2}\, dx=\int \frac{cos\frac{x}{2}\, dx}{sin\frac{x}{2}}=2\int \frac{\frac{1}{2}\, cos\frac{x}{2}\, dx}{sin\frac{x}{2}}=2\int \frac{d(sin\frac{x}{2})}{sin\frac{x}{2}}=\\\\\\=2\cdot ln\Big|\ sin\frac{x}{2}\, \Big|+C$

$P.S.\displaystyle \ \ \ \int \frac{du}{u}=ln|u|+C$