$\int tan x(\sec x - \tan x) dx =$

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

$\int tan x(\sec x - \tan x) dx =$

Options:

sec x - tan x + x - C

sec x - tan²x + x - C

sec x + tan x + x + C

sec x - tan x + C

Correct Answer:

sec x - tan x + x - C

Explanation:

$\int tan x(\sec x - \tan x) dx$

$\int \sec x \tan x dx - \int \tan^2 x dx$

as 1 + tan²x = sec²x

so sec²x - 1 = tan²x

= $\sec x - \int (\sec^2x - 1) dx$

so sec x - tan x + x - C