Tutorial Exercise

Evaluate the integral.

${\displaystyle \underset{0}{\overset{1}{}}}x(9\sqrt[3]{x}+4\sqrt[4]{x})dx$

Step $1$

$To$ find $an$ antiderivative $off(x)=x(9\sqrt[3]{x}+4\sqrt[4]{x}),$ we'll first convert the radicals $to$ fractional powers and then distribute the $x.$

Step $2$

$An$ antiderivative $off(x)=9x^{\frac{4}{3}}+4x^{\frac{5}{4}}is$

$F(x)=,x^{\frac{7}{3}}+,|x$