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

The integral of 7x^{2/5}+4x^{-4/5} is 5x^{7/5}+20x^{1/5}+C

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

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

5 x^{\frac{7}{5}} + 20 x^{\frac{1}{5}} + C

Solution steps

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

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

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

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

\int \frac{4}{x ^{\frac{4}{5}}} d x = 20 x^{\frac{1}{5}}

= 5 x^{\frac{7}{5}} + 20 x^{\frac{1}{5}}

Add a constant to the solution

= 5 x^{\frac{7}{5}} + 20 x^{\frac{1}{5}} + C

\int 6 x 1 + 3^{2} d x

\frac{( ( x + 1 ) ( x + 2 ) )}{x}

x \to - 3 + lim (\frac{- 5 x}{x + 3})

\int \frac{( 4 - ln ∣ x + 3 ∣ ) ^{3}}{x + 3} d x

\frac{d}{d x} (x^{2} \cdot e^{- x})

What is the integral of 7x^{2/5}+4x^{-4/5} ?
The integral of 7x^{2/5}+4x^{-4/5} is 5x^{7/5}+20x^{1/5}+C