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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫  x1  +  x34  dx\int \,\,\frac{{\sqrt x }}{{1\,\, + \,\,\sqrt[4]{{{x^3}}}}}\,\,dx is equal to
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Correct option: B
43  [1+x3/4  −  log⁡e  (1  +  x3/4)]+C\frac{4}{3}\,\,\left[ {1 + {x^{3/4}}\,\, - \,\,{{\log }_e}\,\,\left( {1\,\, + \,\,{x^{3/4}}} \right)} \right] + C
Option B (43  [1+x3/4  −  log⁡e  (1  +  x3/4)]+C\frac{4}{3}\,\,\left[ {1 + {x^{3/4}}\,\, - \,\,{{\log }_e}\,\,\left( {1\,\, + \,\,{x^{3/4}}} \right)} \right] + C) is correct because after substitution and integration, the result matches this option.

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