What is the integral of x+x^9+x^{-9} ?

The integral of x+x^9+x^{-9} is (x^2)/2+(x^{10})/(10)-1/(8x^8)+C

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integral of x+x^9+x^{-9}

\int x + x^{9} + x^{- 9} d x

\frac{x ^{2}}{2} + \frac{x ^{10}}{10} - \frac{1}{8 x ^{8}} + C

Solution steps

\int x + x^{9} + x^{- 9} 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 x d x + \int x^{9} d x + \int x^{- 9} d x

\int x d x = \frac{x ^{2}}{2}

\int x^{9} d x = \frac{x ^{10}}{10}

\int x^{- 9} d x = - \frac{1}{8 x ^{8}}

= \frac{x ^{2}}{2} + \frac{x ^{10}}{10} - \frac{1}{8 x ^{8}}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{x ^{10}}{10} - \frac{1}{8 x ^{8}} + C

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What is the integral of x+x^9+x^{-9} ?
The integral of x+x^9+x^{-9} is (x^2)/2+(x^{10})/(10)-1/(8x^8)+C