JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int\left(\frac{x^2-x+1}{x^2+1}\right) e^{\cot^ {-1}(x)} d x=f(x) \cdot e^{\cot^{-1}(x)}+C

where

C

is constant of integration. Then

f(x)

is equal to:

View answer and explanation

Correct option: C

x

Option C (

x

) is correct because integrating the given expression using substitution

\cot^{-1}x = t

leads to

f(x) = x

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