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

The integral of (\sqrt[6]{x}+\sqrt[7]{x}) is 6/7 x^{7/6}+7/8 x^{8/7}+C

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

\frac{6}{7} x^{\frac{7}{6}} + \frac{7}{8} x^{\frac{8}{7}} + C

Solution steps

Apply the Sum Rule:

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

= \frac{6}{7} x^{\frac{7}{6}} + \frac{7}{8} x^{\frac{8}{7}}

Add a constant to the solution

= \frac{6}{7} x^{\frac{7}{6}} + \frac{7}{8} x^{\frac{8}{7}} + C

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 5

x sin (x)

f (x) = 1 + 8 x

(1 + x^{4})^{\frac{2}{3}}

\frac{d}{d x} (\frac{( 5 x - 3 )}{( 4 x - \frac{3}{x} )})

What is the integral of (\sqrt[6]{x}+\sqrt[7]{x}) ?
The integral of (\sqrt[6]{x}+\sqrt[7]{x}) is 6/7 x^{7/6}+7/8 x^{8/7}+C