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

x \to 2 lim (2 x^{2} - 2 x)

\int x^{2} cot (x^{3}) d x

\frac{\partial}{\partial x} (\frac{3 x}{4 y})

3 x + \frac{5}{x}

\frac{d}{d x} (2^{t a n (4 x)})

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