What is the integral of x(6\sqrt[3]{x}+7\sqrt[4]{x}) ?

The integral of x(6\sqrt[3]{x}+7\sqrt[4]{x}) is 18/7 x^{7/3}+28/9 x^{9/4}+C

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integral of x(6\sqrt[3]{x}+7\sqrt[4]{x})

\frac{18}{7} x^{\frac{7}{3}} + \frac{28}{9} x^{\frac{9}{4}} + C

Solution steps

Expand

= \int 6 x^{\frac{4}{3}} + 7 x^{\frac{5}{4}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 6 x^{\frac{4}{3}} d x + \int 7 x^{\frac{5}{4}} d x

\int 6 x^{\frac{4}{3}} d x = \frac{18}{7} x^{\frac{7}{3}}

\int 7 x^{\frac{5}{4}} d x = \frac{28}{9} x^{\frac{9}{4}}

= \frac{18}{7} x^{\frac{7}{3}} + \frac{28}{9} x^{\frac{9}{4}}

Add a constant to the solution

= \frac{18}{7} x^{\frac{7}{3}} + \frac{28}{9} x^{\frac{9}{4}} + C

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What is the integral of x(6\sqrt[3]{x}+7\sqrt[4]{x}) ?
The integral of x(6\sqrt[3]{x}+7\sqrt[4]{x}) is 18/7 x^{7/3}+28/9 x^{9/4}+C