Question

The value of $\int \frac{1}{1+Cos8x}dx$ is

• A. $\frac{\tan 8x}{8}+C$
• B. $\frac{\tan 2x}{8}+C$
• C. $\frac{\tan 4x}{8}+C$
• D. $\frac{\tan 4x}{4}+C$

Answer 1

Answer: (C)

$I=\int \frac{1}{1+\cos 8x}dx$
$=\int \frac{1}{2{\cos }^{2}4x}dx$
$x=\frac{1}{2}\int {\sec }^{2}4xdx$
$=\frac{1}{2}\frac{\tan 4x}{4}+c$
$=\frac{\tan 4x}{8}+c$