Question

\int \left(x^{\frac{1}{3}}+x^{\frac{-1}{3}}\right)^4dx

Answer 1

$\int \left(x^{\frac{1}{3}}+x^{\frac{-1}{3}}\right)^4dx=\int (x^{\frac{4}{3}}+4*x^{\frac{2}{3}}+6+4*x^{\frac{-2}{3}}+x^{\frac{-4}{3}})dx=\int x^{\frac{4}{3}}dx+\int4*x^{\frac{2}{3}}dx+\int6dx+\int4*x^{\frac{-2}{3}}dx+\int x^{\frac{-4}{3}}dx=\frac{3}{7}*x^{\frac{7}{3}}+\frac{12}{5}*x^{\frac{5}{3}}+6*x+12*x^{\frac{1}{3}}-3*x^{\frac{-1}{3}}+C$