What is the integral of 8x^{3/5}+5x^{-4/5} ?

The integral of 8x^{3/5}+5x^{-4/5} is 5x^{8/5}+25x^{1/5}+C

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integral of 8x^{3/5}+5x^{-4/5}

\int 8 x^{\frac{3}{5}} + 5 x^{- \frac{4}{5}} d x

5 x^{\frac{8}{5}} + 25 x^{\frac{1}{5}} + C

Solution steps

\int 8 x^{\frac{3}{5}} + 5 x^{- \frac{4}{5}} d x

5 x^{- \frac{4}{5}} = \frac{5}{x ^{\frac{4}{5}}}

= \int 8 x^{\frac{3}{5}} + \frac{5}{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 8 x^{\frac{3}{5}} d x + \int \frac{5}{x ^{\frac{4}{5}}} d x

\int 8 x^{\frac{3}{5}} d x = 5 x^{\frac{8}{5}}

\int \frac{5}{x ^{\frac{4}{5}}} d x = 25 x^{\frac{1}{5}}

= 5 x^{\frac{8}{5}} + 25 x^{\frac{1}{5}}

Add a constant to the solution

= 5 x^{\frac{8}{5}} + 25 x^{\frac{1}{5}} + C

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What is the integral of 8x^{3/5}+5x^{-4/5} ?
The integral of 8x^{3/5}+5x^{-4/5} is 5x^{8/5}+25x^{1/5}+C