JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{\left(x^2-1\right) \mathrm{d} x}{\left(x^4+3 x^2+1\right) \tan ^{-1} \frac{x^2+1}{x}}=

\log \left|\tan ^{-1} f(x)\right|+C

then

View answer and explanation

Correct option: D

f(x)=\frac{x^2+1}{x}

Option D (

f(x)=\frac{x^2+1}{x}

) is correct because after dividing the numerator and denominator by

x^2

and using appropriate substitutions, the integral simplifies to

\log |\tan^{-1} (\frac{x^2+1}{x})| + C

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