What is the integral of (7x+6)/(x^9) ?

The integral of (7x+6)/(x^9) is -1/(x^7)-3/(4x^8)+C

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integral of (7x+6)/(x^9)

\int \frac{7 x + 6}{x ^{9}} d x

- \frac{1}{x ^{7}} - \frac{3}{4 x ^{8}} + C

Solution steps

\int \frac{7 x + 6}{x ^{9}} d x

Expand

\frac{7 x + 6}{x ^{9}} : \frac{7}{x ^{8}} + \frac{6}{x ^{9}}

= \int \frac{7}{x ^{8}} + \frac{6}{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{7}{x ^{8}} d x + \int \frac{6}{x ^{9}} d x

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

\int \frac{6}{x ^{9}} d x = - \frac{3}{4 x ^{8}}

= - \frac{1}{x ^{7}} - \frac{3}{4 x ^{8}}

Add a constant to the solution

= - \frac{1}{x ^{7}} - \frac{3}{4 x ^{8}} + C

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What is the integral of (7x+6)/(x^9) ?
The integral of (7x+6)/(x^9) is -1/(x^7)-3/(4x^8)+C