Mathematics

Solve $$\int {{x^{1/3}}\left( {1 + {x^{1/3}}} \right) - 2dx} $$


SOLUTION

Consider the given integral.


$$I=\displaystyle\int{\left[ {{x}^{\dfrac{1}{3}}}\left( 1+{{x}^{\dfrac{1}{3}}} \right)-2 \right]dx}$$


$$ I=\displaystyle\int{\left( {{x}^{\dfrac{1}{3}}}+{{x}^{\dfrac{2}{3}}}-2 \right)dx} $$


$$ I=\dfrac{{{x}^{\dfrac{4}{3}}}}{\dfrac{4}{3}}+\dfrac{{{x}^{\dfrac{5}{3}}}}{\dfrac{5}{3}}-2x+C $$


$$ I=\dfrac{3}{4}{{x}^{\dfrac{4}{3}}}+\dfrac{3}{5}{{x}^{\dfrac{5}{3}}}-2x+C $$


 


Hence, this is the answer.

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Subjective Medium Published on 17th 09, 2020
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