What is the integral of 9x^8-8/(x^8) ?

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

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integral of 9x^8-8/(x^8)

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

x^{9} + \frac{8}{7 x ^{7}} + C

Solution steps

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

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

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

= x^{9} - (- \frac{8}{7 x ^{7}})

Simplify

= x^{9} + \frac{8}{7 x ^{7}}

Add a constant to the solution

= x^{9} + \frac{8}{7 x ^{7}} + C

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