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

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

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

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

\frac{x ^{6}}{6} + \frac{5}{x} + 2 x + C

Solution steps

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

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

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

\int 2 d x = 2 x

= \frac{x ^{6}}{6} - (- \frac{5}{x}) + 2 x

Simplify

= \frac{x ^{6}}{6} + \frac{5}{x} + 2 x

Add a constant to the solution

= \frac{x ^{6}}{6} + \frac{5}{x} + 2 x + C

f (x) = 4 x (x^{2} - 4 x + 5)^{9}, at x = 2

\frac{d}{d x} (9 e^{- 4 x})

y^{3} \frac{d y}{d x} + x^{3} = 0

\frac{\partial}{\partial y} (x^{2} - 4 x y - 2 y^{2})

\int (3 x^{2} - 6 x + 3) d x

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