$\mathop \smallint \nolimits_8^{15} \,\,\frac{{dx}}{{\left( {x - 3} \right)\,\,\sqrt {x + 1} }}$ is equal to

$\frac{1}{3}\,\,\log \,\,\frac{5}{3}$

$\frac{1}{2}\,\,\log \,\,\frac{3}{5}$

$\frac{1}{5}\,\,\log \,\,\frac{3}{5}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\int \nolimits_8^{15} \,\,\frac{{dx}}{{\left( {x - 3} \right)\,\,\sqrt {x + 1} }}

is equal to

View answer and explanation

Correct option: A

\frac{1}{2}\,\,\log \,\,\frac{5}{3}

Option A (

\frac{1}{2}\log \frac{5}{3}

) is correct because the integral evaluates to this value after a suitable trigonometric substitution and simplification.

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