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

The integral of 7x^{2/5}+2x^{-4/5} is 5x^{7/5}+10x^{1/5}+C

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

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

5 x^{\frac{7}{5}} + 10 x^{\frac{1}{5}} + C

Solution steps

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

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

\int 2 x^{- \frac{4}{5}} d x = 10 x^{\frac{1}{5}}

= 5 x^{\frac{7}{5}} + 10 x^{\frac{1}{5}}

Add a constant to the solution

= 5 x^{\frac{7}{5}} + 10 x^{\frac{1}{5}} + C

\frac{d}{d x} (tan (x^{2} + y))

\frac{d}{d x} (3 arcsin (x))

\int \frac{1}{( x ^{2} - 81 ) ^{\frac{3}{2}}} d x

\frac{3}{( s + 2 ) ^{3}}

y = x^{3} - 2 x^{2} + 2, y = 3 x^{2} + 5 x - 23, - 1, 7

What is the integral of 7x^{2/5}+2x^{-4/5} ?
The integral of 7x^{2/5}+2x^{-4/5} is 5x^{7/5}+10x^{1/5}+C