What is the integral of (1+1/2 u^4-2/5 u^9) ?

The integral of (1+1/2 u^4-2/5 u^9) is u+(u^5)/(10)-(u^{10})/(25)+C

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integral of (1+1/2 u^4-2/5 u^9)

\int (1 + \frac{1}{2} u^{4} - \frac{2}{5} u^{9}) d u

u + \frac{u ^{5}}{10} - \frac{u ^{10}}{25} + C

Solution steps

\int 1 + \frac{1}{2} u^{4} - \frac{2}{5} u^{9} 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 1 d u + \int \frac{1}{2} u^{4} d u - \int \frac{2}{5} u^{9} d u

\int 1 d u = u

\int \frac{1}{2} u^{4} d u = \frac{u ^{5}}{10}

\int \frac{2}{5} u^{9} d u = \frac{u ^{10}}{25}

= u + \frac{u ^{5}}{10} - \frac{u ^{10}}{25}

Add a constant to the solution

= u + \frac{u ^{5}}{10} - \frac{u ^{10}}{25} + C

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What is the integral of (1+1/2 u^4-2/5 u^9) ?
The integral of (1+1/2 u^4-2/5 u^9) is u+(u^5)/(10)-(u^{10})/(25)+C