What is the integral of x+x^6+x^{-6} ?

The integral of x+x^6+x^{-6} is (x^2)/2+(x^7)/7-1/(5x^5)+C

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integral of x+x^6+x^{-6}

\int x + x^{6} + x^{- 6} d x

\frac{x ^{2}}{2} + \frac{x ^{7}}{7} - \frac{1}{5 x ^{5}} + C

Solution steps

\int x + x^{6} + x^{- 6} 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^{6} d x + \int x^{- 6} d x

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

\int x^{6} d x = \frac{x ^{7}}{7}

\int x^{- 6} d x = - \frac{1}{5 x ^{5}}

= \frac{x ^{2}}{2} + \frac{x ^{7}}{7} - \frac{1}{5 x ^{5}}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{x ^{7}}{7} - \frac{1}{5 x ^{5}} + C

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What is the integral of x+x^6+x^{-6} ?
The integral of x+x^6+x^{-6} is (x^2)/2+(x^7)/7-1/(5x^5)+C