What is the integral of 10x^9-9/(x^9) ?

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

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integral of 10x^9-9/(x^9)

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

x^{10} + \frac{9}{8 x ^{8}} + C

Solution steps

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

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

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

= x^{10} - (- \frac{9}{8 x ^{8}})

Simplify

= x^{10} + \frac{9}{8 x ^{8}}

Add a constant to the solution

= x^{10} + \frac{9}{8 x ^{8}} + C

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