What is the integral of (1/(x^{3/2)}-x^{4/5}) ?

The integral of (1/(x^{3/2)}-x^{4/5}) is -2/(x^{1/2)}-5/9 x^{9/5}+C

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integral of (1/(x^{3/2)}-x^{4/5})

\int (\frac{1}{x ^{\frac{3}{2}}} - x^{\frac{4}{5}}) d x

- \frac{2}{x ^{\frac{1}{2}}} - \frac{5}{9} x^{\frac{9}{5}} + C

Solution steps

\int \frac{1}{x ^{\frac{3}{2}}} - x^{\frac{4}{5}} 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 \frac{1}{x ^{\frac{3}{2}}} d x - \int x^{\frac{4}{5}} d x

\int \frac{1}{x ^{\frac{3}{2}}} d x = - \frac{2}{x ^{\frac{1}{2}}}

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

= - \frac{2}{x ^{\frac{1}{2}}} - \frac{5}{9} x^{\frac{9}{5}}

Add a constant to the solution

= - \frac{2}{x ^{\frac{1}{2}}} - \frac{5}{9} x^{\frac{9}{5}} + C

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What is the integral of (1/(x^{3/2)}-x^{4/5}) ?
The integral of (1/(x^{3/2)}-x^{4/5}) is -2/(x^{1/2)}-5/9 x^{9/5}+C