The value of $\mathop \smallint \limits_3^5 \,\,\frac{{{x^2}}}{{{x^2} - \,\,4}}\,\,dx$, is

$2\,\, + \,\,4{\log _e}\,\,3\,\,\, - \,\,4\,\,{\log _e}\,\,7 + 4\,\,{\log _e}\,\,5$

$2\,\, - \,\,{\tan ^{ - 1}}\,\,\left( {\frac{{15}}{7}} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of

\int \limits_3^5 \,\,\frac{{{x^2}}}{{{x^2} - \,\,4}}\,\,dx

, is

View answer and explanation

Correct option: B

2\,\, + \,\,{\log _e}\left( {\frac{{15}}{7}} \right)

Option B (

2\,\, + \,\,{\log _e}\left( {\frac{{15}}{7}} \right)

) is correct because evaluating the definite integral using partial fractions yields this result.

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