The integral $\mathop \smallint \nolimits_{ - 1}^3 \,\,\left[ {{{\tan }^{ - 1}}\,\,\frac{x}{{{x^2} + 1}}\,\, + \,\,{{\tan }^{ - 1}}\,\,\frac{{{x^2} + \,\,1}}{x}} \right]\;\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The integral

\int \nolimits_{ - 1}^3 \,\,\left[ {{{\tan }^{ - 1}}\,\,\frac{x}{{{x^2} + 1}}\,\, + \,\,{{\tan }^{ - 1}}\,\,\frac{{{x^2} + \,\,1}}{x}} \right]\;\,\,dx

is equal to

View answer and explanation

Correct option: D

2\,\pi

Option D (

2\pi

) is correct because the integral simplifies to a constant value of

\pi/2

over the interval [-1, 3], resulting in

2\pi

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