Question

Tìm:

a) \(\int\left(1+\cot^2x\right)dx;\)

b) \(\int\dfrac{1}{1+\cos2x}dx.\)

Answer 1

a) \(\int {(1 + {{\cot }^2}x)dx} = \int {\frac{1}{{{{\sin }^2}x}}dx} = - \cot x + C\).

b) \(\int {\frac{1}{{1 + \cos 2x}}dx} = \int {\frac{1}{{1 + (2{{\cos }^2}x - 1)}}dx} = \int {\frac{1}{{2{{\cos }^2}x}}dx} \)

\( = \frac{1}{2}\int {\frac{1}{{{{\cos }^2}x}}dx} = \frac{1}{2}\tan x + C\).