$\mathop \smallint \limits_1^{\frac{{4\sqrt 3 }}{5} - 1} \,\,\frac{{x + 2}}{{\sqrt {{x^2} + 2x - 3} }}\,\,dx$ equals to

$\frac{{2\,\sqrt 3 }}{3}\,\, - \,\,\frac{1}{2}\,\,\log \,\,\left( {\sqrt 3 + 2} \right)$

$\frac{{2\,\sqrt 3 }}{3}\,\, + \,\,\frac{1}{2}\,\,\log \,\,\left( {\sqrt 3 + 2} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Hard

1 of 1

Application +4 | -1

\int \limits_1^{\frac{{4\sqrt 3 }}{5} - 1} \,\,\frac{{x + 2}}{{\sqrt {{x^2} + 2x - 3} }}\,\,dx

equals to

View answer and explanation

Correct option: B

\frac{{2\,\sqrt 3 }}{3}\,\, + \,\,\frac{1}{2}\,\,\log \,\,3

Option B (

\frac{{2\,\sqrt 3 }}{3}\,\,+\,\,\frac{1}{2}\,\,\log \,3

) is correct because it is the result of evaluating the definite integral after proper substitution and simplification.

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