What is the integral of \sqrt[5]{x}(1-sqrt(x)) ?

The integral of \sqrt[5]{x}(1-sqrt(x)) is 5/6 x^{6/5}-10/17 x^{17/10}+C

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integral of \sqrt[5]{x}(1-sqrt(x))

\frac{5}{6} x^{\frac{6}{5}} - \frac{10}{17} x^{\frac{17}{10}} + C

Solution steps

Expand

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{7}{10}} d x = \frac{10}{17} x^{\frac{17}{10}}

= \frac{5}{6} x^{\frac{6}{5}} - \frac{10}{17} x^{\frac{17}{10}}

Add a constant to the solution

= \frac{5}{6} x^{\frac{6}{5}} - \frac{10}{17} x^{\frac{17}{10}} + C

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

n = 0 \sum \infty (0.1)^{n}

\frac{d}{d x} (cos^{3} (x^{2} - x))

\int cos (m) y d y

What is the integral of \sqrt[5]{x}(1-sqrt(x)) ?
The integral of \sqrt[5]{x}(1-sqrt(x)) is 5/6 x^{6/5}-10/17 x^{17/10}+C