Q. The value of the integral $\int \frac{s e c x}{s i n x + c o s x} d x$ is

165 161 Integrals Report Error

A

$ln ∣1 + tan x ∣ + C$

60%

B

$ln ∣ tan x ∣ + C$

17%

C

$tan^{- 1} (1 + tan x) + C$

8%

D

$ln ∣ sin x + cos x ∣ \cdot sec x + C$

15%

Solution:

$\int \frac{d x}{c o s ^{2} x ( 1 + t a n x )} = \int \frac{s e c ^{2} x}{1 + t a n x} d x = ln ∣1 + tan x ∣ + C$