What is the integral of u^{-5}(7-u^5+u^{10}) ?

The integral of u^{-5}(7-u^5+u^{10}) is -7/(4u^4)-u+(u^6)/6+C

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integral of u^{-5}(7-u^5+u^{10})

\int u^{- 5} (7 - u^{5} + u^{10}) d u

- \frac{7}{4 u ^{4}} - u + \frac{u ^{6}}{6} + C

Solution steps

\int u^{- 5} (7 - u^{5} + u^{10}) d u

Expand

u^{- 5} (7 - u^{5} + u^{10}) : \frac{7}{u ^{5}} - 1 + u^{5}

= \int \frac{7}{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{7}{u ^{5}} d u - \int 1 d u + \int u^{5} d u

\int \frac{7}{u ^{5}} d u = - \frac{7}{4 u ^{4}}

\int 1 d u = u

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

= - \frac{7}{4 u ^{4}} - u + \frac{u ^{6}}{6}

Add a constant to the solution

= - \frac{7}{4 u ^{4}} - u + \frac{u ^{6}}{6} + C

\frac{d y}{d x} - 12 y = e^{9 x} y^{2}

\frac{\partial}{\partial x} (4 x y e^{x - y^{2}})

x \to 0 lim (e^{x^{2}} - 1)

\frac{d y}{d x} = x^{2} - y - 2, y (0) = 1

\int 5 x^{\frac{3}{2}} + 2 x d x

What is the integral of u^{-5}(7-u^5+u^{10}) ?
The integral of u^{-5}(7-u^5+u^{10}) is -7/(4u^4)-u+(u^6)/6+C