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

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

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

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

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

Solution steps

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

Expand

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

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

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

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

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

Simplify

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

Add a constant to the solution

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

4 x^{3} - 3 x^{2} + 4, at x = 2

\frac{d y}{d x} = 2 y - x^{2}

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

\frac{\partial}{\partial x} (\frac{5}{e ^{x}})

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