What is the integral of (y^{2/3}-4y^{-1/5}+4) ?

The integral of (y^{2/3}-4y^{-1/5}+4) is 3/5 y^{5/3}-5y^{4/5}+4y+C

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integral of (y^{2/3}-4y^{-1/5}+4)

\int (y^{\frac{2}{3}} - 4 y^{- \frac{1}{5}} + 4) d y

\frac{3}{5} y^{\frac{5}{3}} - 5 y^{\frac{4}{5}} + 4 y + C

Solution steps

\int y^{\frac{2}{3}} - 4 y^{- \frac{1}{5}} + 4 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int y^{\frac{2}{3}} d y - \int 4 y^{- \frac{1}{5}} d y + \int 4 d y

\int y^{\frac{2}{3}} d y = \frac{3}{5} y^{\frac{5}{3}}

\int 4 y^{- \frac{1}{5}} d y = 5 y^{\frac{4}{5}}

\int 4 d y = 4 y

= \frac{3}{5} y^{\frac{5}{3}} - 5 y^{\frac{4}{5}} + 4 y

Add a constant to the solution

= \frac{3}{5} y^{\frac{5}{3}} - 5 y^{\frac{4}{5}} + 4 y + C

\frac{d}{d x} (ln (\frac{x + 1}{x - 3}))

f (x) = \frac{5}{x ^{3}}

\int 8 u^{\frac{7}{2}} d u

5^{x}, 0

y = (x^{4} + 2)^{2} (x^{5} + 4)^{4}

What is the integral of (y^{2/3}-4y^{-1/5}+4) ?
The integral of (y^{2/3}-4y^{-1/5}+4) is 3/5 y^{5/3}-5y^{4/5}+4y+C