Question

Evaluate \[ \int \frac{\tan 2x}{\cos^4 x}\,dx \]

• A. \(\tan^2x-\log\!\left(1-\tan^2x\right)^2+c\)
• B. \(-\tan^2x-\log\!\left(1-\tan^2x\right)^2+c\)
• C. \(-\tan^2x+\log\!\left(1-\tan^2x\right)+c\)
• D. \(\tan^2x+\log\!\left(1-\tan^2x\right)+c\)

Hint:

For integrals involving \[ \tan x,\qquad \sec x, \] use the substitution \[ \boxed{t=\tan x.} \] Also remember \[ \boxed{\tan2x=\frac{2\tan x}{1-\tan^2x}}. \]

Answer 1

The Correct Option is B