What is the integral of (8x^5-8x^{-3}) ?

The integral of (8x^5-8x^{-3}) is (4x^6)/3+4/(x^2)+C

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integral of (8x^5-8x^{-3})

\int (8 x^{5} - 8 x^{- 3}) d x

\frac{4 x ^{6}}{3} + \frac{4}{x ^{2}} + C

Solution steps

\int 8 x^{5} - 8 x^{- 3} 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 8 x^{5} d x - \int 8 x^{- 3} d x

\int 8 x^{5} d x = \frac{4 x ^{6}}{3}

\int 8 x^{- 3} d x = - \frac{4}{x ^{2}}

= \frac{4 x ^{6}}{3} - (- \frac{4}{x ^{2}})

Simplify

= \frac{4 x ^{6}}{3} + \frac{4}{x ^{2}}

Add a constant to the solution

= \frac{4 x ^{6}}{3} + \frac{4}{x ^{2}} + C

What is the integral of (8x^5-8x^{-3}) ?
The integral of (8x^5-8x^{-3}) is (4x^6)/3+4/(x^2)+C