What is the integral of u^{-5}(8-u^5+u^{10}) ?

The integral of u^{-5}(8-u^5+u^{10}) is -2/(u^4)-u+(u^6)/6+C

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integral of u^{-5}(8-u^5+u^{10})

\int u^{- 5} (8 - u^{5} + u^{10}) d u

- \frac{2}{u ^{4}} - u + \frac{u ^{6}}{6} + C

Solution steps

\int u^{- 5} (8 - u^{5} + u^{10}) d u

Expand

u^{- 5} (8 - u^{5} + u^{10}) : \frac{8}{u ^{5}} - 1 + u^{5}

= \int \frac{8}{u ^{5}} - 1 + u^{5} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{8}{u ^{5}} d u - \int 1 d u + \int u^{5} d u

\int \frac{8}{u ^{5}} d u = - \frac{2}{u ^{4}}

\int 1 d u = u

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

= - \frac{2}{u ^{4}} - u + \frac{u ^{6}}{6}

Add a constant to the solution

= - \frac{2}{u ^{4}} - u + \frac{u ^{6}}{6} + C

n \to \infty lim ((n + 1) x)

\frac{3 x - 9}{2 x + 8}

t^{- 3}

\frac{d}{d x} (cos^{3} (\frac{x ^{2}}{1 - x}))

x \to - 2 lim (\frac{1}{2 - x})

What is the integral of u^{-5}(8-u^5+u^{10}) ?
The integral of u^{-5}(8-u^5+u^{10}) is -2/(u^4)-u+(u^6)/6+C