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

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

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

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

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

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 after substituting

x + 1 = t^2

and evaluating the definite integral, the result is

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

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