Question

If $f(x)$ is a quadratic expression such that $f(0)=f(1)=3 f(2)=-3$, then $\int \frac{f(x)}{x^3-1} d x=$

Accepted Answer

$\log _e|x-1|+\log _e\left(x^2+x+1\right)+\frac{2}{\sqrt{3}} \operatorname{Tan}^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c$

Answer

$\log _e|x-1|+\log _e\left(x^2+x+1\right)+\frac{1}{\sqrt{3}} \operatorname{Tan}^{-1}\left(\frac{x+1}{\sqrt{3}}\right)+c$

Answer

$\log _e\left(x^2+x+1\right)+\log _e|x|+\frac{2}{\sqrt{3}} \operatorname{Tan}^{-1}\left(\frac{2 x+3}{\sqrt{3}}\right)+c$

Answer

$\log _e\left|x^3+x^2+x\right|+\frac{2}{\sqrt{3}} \operatorname{Tan}^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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