What is the integral of u^{-5}(2-u^5+u^{10}) ?

The integral of u^{-5}(2-u^5+u^{10}) is -(2-u^5+u^{10}}{4u^4}+5/4 (\frac{u^6)/3-u)+C

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integral of u^{-5}(2-u^5+u^{10})

\int u^{- 5} (2 - u^{5} + u^{10}) d u

- \frac{2 - u ^{5} + u ^{10}}{4 u ^{4}} + \frac{5}{4} (\frac{u ^{6}}{3} - u) + C

Solution steps

\int u^{- 5} (2 - u^{5} + u^{10}) d u

Apply Integration By Parts

: - \frac{2 - u ^{5} + u ^{10}}{4 u ^{4}} - \int - \frac{5}{4} (2 u^{5} - 1) d u

= - \frac{2 - u ^{5} + u ^{10}}{4 u ^{4}} - \int - \frac{5}{4} (2 u^{5} - 1) d u

\int - \frac{5}{4} (2 u^{5} - 1) d u = - \frac{5}{4} (\frac{u ^{6}}{3} - u)

= - \frac{2 - u ^{5} + u ^{10}}{4 u ^{4}} - (- \frac{5}{4} (\frac{u ^{6}}{3} - u))

Simplify

= - \frac{2 - u ^{5} + u ^{10}}{4 u ^{4}} + \frac{5}{4} (\frac{u ^{6}}{3} - u)

Add a constant to the solution

= - \frac{2 - u ^{5} + u ^{10}}{4 u ^{4}} + \frac{5}{4} (\frac{u ^{6}}{3} - u) + C

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What is the integral of u^{-5}(2-u^5+u^{10}) ?
The integral of u^{-5}(2-u^5+u^{10}) is -(2-u^5+u^{10}}{4u^4}+5/4 (\frac{u^6)/3-u)+C