Question

If $\smallint \,\,\frac{{\log \,\,\left( {x\,\, + \,\,\sqrt {1\,\, + \,\,{x^2}} } \right)}}{{\sqrt {1\,\, + \,\,{x^2}} }}\;\,\,dx = {\rm{g}}\,\,of\,\,\left( x \right) + $ constant, then

Accepted Answer

$f\,\,\left( x \right) = \log \,\,\left( {x + \sqrt {{x^2} + \,\,1} } \right)$ and ${\rm{g}}\,\,\left( x \right) = \frac{{{x^2}}}{2}$

Answer

$f\,\,\left( x \right) = \log \,\,(x + \sqrt {{x^2} + \,\,1} )$

Answer

$f\left( x \right) = \log \,\,\left( {x + \sqrt {{x^2} + \,\,1} } \right)$ and ${\rm{g}}\,\,\left( x \right) = {x^2}$

Answer

$f\,\,\left( x \right) = \frac{{{x^2}}}{2}$ and ${\rm{g}}\,\,\left( x \right) = \log \,\,\left( {x\,\, + \,\,\sqrt {{x^2} + \,\,1} } \right)$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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