Question

The value of the integral $\smallint \,\,\frac{{\log \,\,\left( {x + 1} \right) - \log \,\,x}}{{x\left( {x + 1} \right)}}\,\,dx$ is

Accepted Answer

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

Answer

$ - \,\,\left[ {{{\left\{ {\log \left( {x + 1} \right)} \right\}}^2} - \,\,{{\left( {\log \,\,x} \right)}^2}} \right]\,\, + \,\,\log \,\,\left( {x + 1} \right)\log \,\,x + \,\,c$

Answer

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

Answer

None of the above

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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