Question

Utilizand metoda integrarii prin parti, calculati integralele:
integrala din: x/sin^2(x) dx =

Answer 1

$=\int x(-\cot x)'\ dx=-x\cot x +\int \cot x \ dx$

Luam a doua integrala si o rezolvam prin schimbare de variabila
 $t=\sin x\\ dt=\cos x \ dx$

$\int \cot x \ dx=\int\dfrac{\cos x}{\sin x}dx=\int\dfrac{dt}{t}=\ln t=\ln(\sin x).$

Raspunsul final e:

$-x\cot x+\ln(\sin x)+C$