Question

If $f\left( x \right) = \frac{{x + 2}}{{2x + 3}}$. Then, $\smallint \,{\left( {\frac{{f\left( x \right)}}{{{x^2}}}} \right)^{1/2}}dx$ is equal to $\frac{1}{{\sqrt 2 }}\,\,{\rm{g}}\left( {\frac{{1 + \sqrt {2f\left( x \right)} }}{{1 - \sqrt {2f\left( x \right)} }}} \right)\,\, - \,\,\sqrt {\frac{2}{3}} \,\,h\left( {\frac{{\sqrt {3\,f\left( x \right)} \,\, + \,\,\sqrt 2 }}{{\sqrt {3\,f\left( x \right)} \,\, - \,\,\sqrt 2 }}} \right) + \,\,c$ where

Accepted Answer

${\rm{g}}\left( x \right) = \log \,\,\left| {\,x\,} \right|,\,\,\;h\left( x \right) = \log \,\,\left| {\,x\,} \right|$

Answer

${m{g}}\,\left( x ight) = {	an ^{ - 1}}x,\;\,\,h\left( x ight) = \log \,\,\left| {\,x\,} ight|$

Answer

${m{g}}\,\left( x ight) = \log \,\,\left| {\,x\,} ight|,\;\,\,h\left( x ight) = {	an ^{ - 1}}\,\,x$

Answer

${m{g}}\left( x ight) = h\left( x ight) = {	an ^{ - 1}}x$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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