Tính nguyên hàm \(\int {\dfrac{{1 - 2{{\tan }^2}x}...

A

- Hướng dẫn giải

Ta có:

\(\begin{array}{l}\int {\dfrac{{1 - 2{{\tan }^2}x}}{{{{\sin }^2}x}}\,dx} \\ = \int {\left( {\dfrac{1}{{{{\sin }^2}x}} - \dfrac{2}{{{{\cos }^2}x}}} \right)\,dx} \\ = \int {\dfrac{1}{{{{\sin }^2}x}}\,dx - 2\int {\dfrac{1}{{{{\cos }^2}x}}dx} } \\ =  - \cot x - 2\tan x + C\end{array}\)