Tìm nguyên hàm: I=∫sin^4 x / cos^2 x dx

* Hướng dẫn giải

Chọn B.

$I=\int \frac{{\sin }^{4}x}{{\cos }^{2}x}dx$

$$\begin{gathered} =\int \left(\frac{1}{{\cos }^{2}x}+{\cos }^{2}x-2\right)dx \\ =\tan x -2x+\int \frac{dx}{2}+\frac{1}{4}\int \cos 2xd\left(2x\right) \\ =\tan x-\frac{3}{2}x+\frac{1}{4}\sin 2x+C \end{gathered}$$

= tanx - 1,5x + 0,25 sin2x + C