What is the integral of (x^8+1/(x^8)) ?

The integral of (x^8+1/(x^8)) is (x^9)/9-1/(7x^7)+C

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integral of (x^8+1/(x^8))

\int (x^{8} + \frac{1}{x ^{8}}) d x

\frac{x ^{9}}{9} - \frac{1}{7 x ^{7}} + C

Solution steps

\int x^{8} + \frac{1}{x ^{8}} 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^{8} d x + \int \frac{1}{x ^{8}} d x

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

\int \frac{1}{x ^{8}} d x = - \frac{1}{7 x ^{7}}

= \frac{x ^{9}}{9} - \frac{1}{7 x ^{7}}

Add a constant to the solution

= \frac{x ^{9}}{9} - \frac{1}{7 x ^{7}} + C

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What is the integral of (x^8+1/(x^8)) ?
The integral of (x^8+1/(x^8)) is (x^9)/9-1/(7x^7)+C