The value of $\int \tan ^2 x dx$ is : w

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

The value of $\int \tan ^2 x dx$ is :

where C is the constant of integration.

Options:

$\sec ^2 x+C$

$\tan x-x+C$

$\sec x+x+C$

$\tan x+x+C$

Correct Answer:

$\tan x-x+C$

Explanation:

$I=\int \tan ^2 x d x$

$I=\int\left(\sec ^2 x-1\right) d x$ ← $1+\tan ^2 x=\sec ^2 x \Rightarrow \tan ^2 x=\sec ^2 x-1$

$I=\tan x-x+C$ ← $\int \sec ^2 x d x=\tan x$