question_answer

\[\int{\sqrt[3]{x}}\sqrt{1+\sqrt[3]{{{x}^{4}}}}\,dx\] is equal to

A)  \[\frac{7}{32}\,\,{{\left( 1+\sqrt[3]{{{x}^{4}}} \right)}^{\frac{8}{7}}}+c\]

B)  \[\frac{21}{32}\,\,{{\left( 1+\sqrt[3]{{{x}^{4}}} \right)}^{\frac{8}{7}}}+c\]

C)  \[\frac{32}{31}\,\,{{\left( 1+\sqrt[3]{{{x}^{4}}+1} \right)}^{\frac{8}{7}}}+c\]

D)  \[\frac{7}{31}\,\,{{\left( 1+\sqrt[3]{{{x}^{4}}+1} \right)}^{\frac{8}{7}}}+c\]

E)  None of these