$\int_\limits 0^1 \tan ^{-1}\left(\frac{1}{x^2-x+1}\right) d x$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int\limits_{0}^1 \tan ^{-1}\left(\frac{1}{x^2-x+1}\right) d x

View answer and explanation

Correct option: D

\frac{\pi}{2}-\ln 2

Option D (

\frac{{\pi}}{{2}}-\ln 2

) is correct because it is the result of evaluating the definite integral using properties of inverse trigonometric functions and integration by parts.

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