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

The integral of (x^7-5x^{-2}+4) is (x^8)/8+5/x+4x+C

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

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

\frac{x ^{8}}{8} + \frac{5}{x} + 4 x + C

Solution steps

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

\int x^{7} d x = \frac{x ^{8}}{8}

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

\int 4 d x = 4 x

= \frac{x ^{8}}{8} - (- \frac{5}{x}) + 4 x

Simplify

= \frac{x ^{8}}{8} + \frac{5}{x} + 4 x

Add a constant to the solution

= \frac{x ^{8}}{8} + \frac{5}{x} + 4 x + C

What is the integral of (x^7-5x^{-2}+4) ?
The integral of (x^7-5x^{-2}+4) is (x^8)/8+5/x+4x+C