What is the integral of \sqrt[7]{x}+1/(\sqrt[7]{x)} ?

The integral of \sqrt[7]{x}+1/(\sqrt[7]{x)} is 7/8 x^{8/7}+7/6 x^{6/7}+C

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integral of \sqrt[7]{x}+1/(\sqrt[7]{x)}

\int 7 x + \frac{1}{7 x} d x

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

Solution steps

\int 7 x + \frac{1}{7 x} 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 7 x d x + \int \frac{1}{7 x} d x

\int 7 x d x = \frac{7}{8} x^{\frac{8}{7}}

\int \frac{1}{7 x} d x = \frac{7}{6} x^{\frac{6}{7}}

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

Add a constant to the solution

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

\int_{0}^{t} x e^{- x^{2}} d x

(\frac{x ^{4}}{8} + \frac{1}{4 x ^{2}})^{^{'}}

\frac{d}{d x} (e^{\frac{x ^{2}}{2}} x)

\int e^{- 3 y} d y

x \to 6 lim (x + 6)

What is the integral of \sqrt[7]{x}+1/(\sqrt[7]{x)} ?
The integral of \sqrt[7]{x}+1/(\sqrt[7]{x)} is 7/8 x^{8/7}+7/6 x^{6/7}+C