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

\frac{\partial}{\partial x} (\frac{( 2 x - y )}{5 x + 3 y})

x^{2} y^{^{''}} + x y^{^{'}} - y = ln (x)

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

\frac{d}{d x} (\frac{1}{1 + 24 e ^{- 0.28 x}})

\int_{2}^{4} x^{2} d x

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