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

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

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

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

Solution steps

Expand

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

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

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

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

Add a constant to the solution

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

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4 x^{2} ln (4 x)

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