$\mathop \smallint \nolimits_0^1 \,\,{\cot ^{ - 1}}\,\,\left( {1 - x + {x^2}} \right)\;\,\,dx$ is equal to

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \nolimits_0^1 \,\,{\cot ^{ - 1}}\,\,\left( {1 - x + {x^2}} \right)\;\,\,dx

is equal to

View answer and explanation

Correct option: D

\frac{\pi }{2}\,\, - \,\,\log \,\,2

Option D (

\frac{\pi }{2}\, - \,\log \,2

) is correct because after rewriting the integral and using integration by parts, the result is

\frac{\pi}{2} - \log 2

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