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

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

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

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

\frac{x ^{3}}{3} + \frac{1}{4 x ^{4}} + 2 x + C

Solution steps

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

\int x^{2} d x = \frac{x ^{3}}{3}

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

\int 2 d x = 2 x

= \frac{x ^{3}}{3} - (- \frac{1}{4 x ^{4}}) + 2 x

Simplify

= \frac{x ^{3}}{3} + \frac{1}{4 x ^{4}} + 2 x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{1}{4 x ^{4}} + 2 x + C

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