What is the integral of x^{-2}+x^{1/5} ?

The integral of x^{-2}+x^{1/5} is -1/x+5/6 x^{6/5}+C

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integral of x^{-2}+x^{1/5}

\int x^{- 2} + x^{\frac{1}{5}} d x

- \frac{1}{x} + \frac{5}{6} x^{\frac{6}{5}} + C

Solution steps

\int x^{- 2} + x^{\frac{1}{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 x^{- 2} d x + \int x^{\frac{1}{5}} d x

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

\int x^{\frac{1}{5}} d x = \frac{5}{6} x^{\frac{6}{5}}

= - \frac{1}{x} + \frac{5}{6} x^{\frac{6}{5}}

Add a constant to the solution

= - \frac{1}{x} + \frac{5}{6} x^{\frac{6}{5}} + C

\frac{d}{d x} (arctan (s x))

\frac{d}{d x} (tan (x - y))

3 cos (8 t)

y^{^{''}} - 2 y - 8 y = 0, y (0) = - 2, y^{^{'}} (0) = 4

What is the integral of x^{-2}+x^{1/5} ?
The integral of x^{-2}+x^{1/5} is -1/x+5/6 x^{6/5}+C