Question

$\smallint \,\,\frac{{\sqrt {{x^2} + \,\,1} \,\,\left[ {\log \,\,\left( {{x^2} + 1} \right) - 2\,\,\log \,\,x} \right]}}{{{x^4}}}\,\,dx$ is equal to

Accepted Answer

$ - \frac{1}{3}\,\,{\left( {1\,\, + \,\,\frac{1}{{{x^2}}}} \right)^{3/2}}\,\,\left[ {\log \,\,\left( {1\,\, + \,\,\frac{1}{{{x^2}}}} \right)\,\, - \,\,\frac{2}{3}} \right] + C$

Answer

$\frac{1}{3}\,\,{\left( {1\,\, + \,\,\frac{1}{{{x^2}}}} \right)^{1/2}}\,\,\left[ {\log \,\,\left( {1\,\, + \,\,\frac{1}{{{x^2}}}} \right)\,\, + \,\,\frac{2}{3}} \right] + C$

Answer

$\frac{2}{3}\,\,{\left( {1\,\, + \,\,\frac{1}{{{x^2}}}} \right)^{3/2}}\,\,\left[ {\log \,\,\left( {1\,\, + \,\,\frac{1}{{{x^2}}}} \right)\,\, + \,\,\frac{2}{3}} \right] + C$

Answer

None of these

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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