Question

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

Answer 1

Consider the given integral.

$I=\int [x^{\frac{1}{3}}(1+x^{\frac{1}{3}})-2]dx$

$I=\int (x^{\frac{1}{3}}+x^{\frac{2}{3}}-2)dx$

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

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

Hence, this is the answer.