Question

Let $f\left( x \right) = \frac{x}{{{{\left( {1 + {x^n}} \right)}^{1/n}}}}$ for $n\,\, \ge 2$ and ${\rm{g}}\,\,\left( x \right) = \left( {fofo\,\, \ldots of} \right)\,\,\left( x \right)$. $g(x) = \underbrace {(fofo....of)}_{n\,\,times}\,\,(x)$ Then, $\smallint \,\,{x^{n - 2}}\,\,{\rm{g}}\left( x \right)\,\,dx$ equals

Accepted Answer

$\frac{1}{{n\left( {n - 1} \right)}}\,\,{\left( {1 + n{x^n}} \right)^{1 - \frac{1}{n}}}\,\, + \,\,c$

Answer

$\frac{1}{{n - 1}}\,\,{\left( {1 + n{x^n}} \right)^{1 - \frac{1}{n}}}\,\, + \,\,c$

Answer

$\frac{1}{{n\left( {n + 1} \right)}}\,\,{\left( {1 + n{x^n}} \right)^{1 + \frac{1}{n}}}\,\, + \,\,c$

Answer

$\frac{1}{{n + 1}}\,\,{\left( {1 + n{x^n}} \right)^{1 + \frac{1}{n}}}\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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