$\smallint \,\,\frac{{\cos \,\,2x\,\, + \,\,2\,\,{{\sin }^2}\,\,x}}{{{{\cos }^2}\,\,x}}\,\,dx$ is equal to

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \,\,\frac{{\cos \,\,2x\,\, + \,\,2\,\,{{\sin }^2}\,\,x}}{{{{\cos }^2}\,\,x}}\,\,dx

is equal to

View answer and explanation

Correct option: C

\tan \,\,x\,\, + \,\,c

Option C (tan x + c) is correct because simplifying the integrand using trigonometric identities results in sec²x, whose integral is tan x + c.

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