What is the integral of ((x-4)/(x^9)) ?

The integral of ((x-4)/(x^9)) is -1/(7x^7)+1/(2x^8)+C

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integral of ((x-4)/(x^9))

\int (\frac{x - 4}{x ^{9}}) d x

- \frac{1}{7 x ^{7}} + \frac{1}{2 x ^{8}} + C

Solution steps

\int \frac{x - 4}{x ^{9}} d x

Expand

\frac{x - 4}{x ^{9}} : \frac{1}{x ^{8}} - \frac{4}{x ^{9}}

= \int \frac{1}{x ^{8}} - \frac{4}{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 \frac{1}{x ^{8}} d x - \int \frac{4}{x ^{9}} d x

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

\int \frac{4}{x ^{9}} d x = - \frac{1}{2 x ^{8}}

= - \frac{1}{7 x ^{7}} - (- \frac{1}{2 x ^{8}})

Simplify

= - \frac{1}{7 x ^{7}} + \frac{1}{2 x ^{8}}

Add a constant to the solution

= - \frac{1}{7 x ^{7}} + \frac{1}{2 x ^{8}} + C

y = (x - 2)^{2}, y = 4 - x, y = 2 x - 2

\frac{d}{d x} (\frac{75}{12 + x ^{2} + y ^{2}})

\int \frac{- 2 x}{x ^{2} + 4} d x

x \to 3 lim (x 18 - x^{2})

\frac{d}{d x} ((x^{2} + 1) (x^{3} + 1))

What is the integral of ((x-4)/(x^9)) ?
The integral of ((x-4)/(x^9)) is -1/(7x^7)+1/(2x^8)+C