Question

Solve:
$\int \frac{2-3\sin x}{{\cos }^{2}x}dx.$

Answer 1

$\int \frac{(2-3sinx)}{co{s}^{2}x}dx$

$=\int (\frac{2}{{\cos }^{2}x}-\frac{3\sin x}{{\cos }^{2}x})dx$

$=\int 2{\sec }^{2}xdx-\int 3\frac{\sin x}{\cos x}\frac{1}{\cos x}dx$

$=2\int {\sec }^{2}xdx-3\int \sec x\tan xdx$

$=2\mathrm{tanx}-3secx+C$

Hence, this is the answer.