JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \frac{d x}{5-4 \sin x+3 \cos x}

is equal to

\frac{1}{2+f(x)}+C

then

f(x)

is equal to

View answer and explanation

Correct option: C

-\tan \frac{x}{2}

Option C is correct because after applying the tangent half-angle substitution and simplifying, the integral evaluates to

\frac{1}{2-\tan \frac{x}{2}}+C

, thus

f(x) = -\tan \frac{x}{2}

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