Question

Tìm:

a) \(\int\left(3\cos x-4\sin x\right)dx;\)                       b) \(\int\left(\dfrac{1}{\cos^2x}-\dfrac{1}{\sin^2x}\right)dx.\)

Answer 1

a) \(\int {\left( {3\cos x - 4\sin x} \right)dx}  = 3\int {\cos x} dx - 4\int {\sin x} dx = 3\sin x + 4\cos x + C\);

b) \(\int {\left( {\frac{1}{{{{\cos }^2}x}} - \frac{1}{{{{\sin }^2}x}}} \right)dx}  = \int {\frac{1}{{{{\cos }^2}x}}} dx - \int {\frac{1}{{{{\sin }^2}x}}} dx = \tan x + \cot x + C\).