Question

If $I = \smallint \,\,\frac{{{x^5}}}{{\sqrt {1\,\, + \,\,{x^3}} }}\,\,dx$, then $I$ is equal to

Accepted Answer

$\frac{2}{9}\,\,{\left( {1 + {x^3}} \right)^{\frac{3}{2}}}\,\, - \,\,\frac{2}{3}\,\,{\left( {1 + {x^3}} \right)^{\frac{1}{2}}}\,\, + \,\,c$

Answer

$\frac{2}{9}\,\,{\left( {1 + {x^3}} \right)^{\frac{5}{2}}}\,\, + \,\,\frac{2}{3}\,\,{\left( {1 + {x^3}} \right)^{\frac{3}{2}}}\,\, + \,\,c$

Answer

$\log \,\,\left| {\,\,\sqrt x \,\, + \,\,\sqrt {1 + {x^3}} \,} \right|\,\, + \,\,c$

Answer

$\log \,\,\left| {\,\sqrt x \,\, - \,\,\sqrt {1 - {x^3}} \,} \right| + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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