JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int \frac{d x}{\left(x^2-4\right) \sqrt{x+1}}=\frac{1}{k} \log _e\left|\frac{\sqrt{x+1}-\sqrt{3}}{\sqrt{x+1}+\sqrt{3}}\right|

-\frac{1}{2} \operatorname{Tan}^{-1} \sqrt{x+1}+c

then

k

equals

View answer and explanation

Correct option: B

4 \sqrt{3}

Option B (

4 \sqrt{3}

) is correct because after applying a trigonometric substitution and simplifying, the constant

k

is found to be

4 \sqrt{3}

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