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

The integral of 7x^{2/5}+5x^{-4/5} is 5x^{7/5}+25x^{1/5}+C

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

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

5 x^{\frac{7}{5}} + 25 x^{\frac{1}{5}} + C

Solution steps

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

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

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

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

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

= 5 x^{\frac{7}{5}} + 25 x^{\frac{1}{5}}

Add a constant to the solution

= 5 x^{\frac{7}{5}} + 25 x^{\frac{1}{5}} + C

(0, 4), (2, - 3)

\int e^{2 i x} d x

\int_{2}^{3} (y^{2} - 2 y + 1) d y

\frac{d}{d t} (\frac{3 t}{1 + t ^{3}})

x \to 0 + lim (ln (4 sin (x)))

What is the integral of 7x^{2/5}+5x^{-4/5} ?
The integral of 7x^{2/5}+5x^{-4/5} is 5x^{7/5}+25x^{1/5}+C