Question

$\int \frac{x(x-1)}{\left(x^2+1\right)(x+1) \sqrt{x^3+x^2+x}} d x$ is equal to

Accepted Answer

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

Answer

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

Answer

$\frac{1}{4} \log _e\left(\frac{x^2+x+1}{x^2-x+1}\right)+\operatorname{Tan}^{-1}\left(\frac{x^2+x+1}{x}\right)+c$

Answer

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

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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