What is the integral of (7x^{2/5}+8x^{-4/5}) ?

The integral of (7x^{2/5}+8x^{-4/5}) is 5x^{7/5}+40x^{1/5}+C

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integral of (7x^{2/5}+8x^{-4/5})

\int (7 x^{\frac{2}{5}} + 8 x^{- \frac{4}{5}}) d x

5 x^{\frac{7}{5}} + 40 x^{\frac{1}{5}} + C

Solution steps

\int 7 x^{\frac{2}{5}} + 8 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 7 x^{\frac{2}{5}} d x + \int 8 x^{- \frac{4}{5}} d x

\int 7 x^{\frac{2}{5}} d x = 5 x^{\frac{7}{5}}

\int 8 x^{- \frac{4}{5}} d x = 40 x^{\frac{1}{5}}

= 5 x^{\frac{7}{5}} + 40 x^{\frac{1}{5}}

Add a constant to the solution

= 5 x^{\frac{7}{5}} + 40 x^{\frac{1}{5}} + C

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What is the integral of (7x^{2/5}+8x^{-4/5}) ?
The integral of (7x^{2/5}+8x^{-4/5}) is 5x^{7/5}+40x^{1/5}+C