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

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

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

\int \frac{x ^{3} - x}{( x ^{4} - 2 x ^{2} + 3 ) ^{2}} d x

\int 2 t^{- 4} d t

\frac{d}{d x} (x^{6} - 3 x^{5} + 10 x^{3} - 15 x^{2} + 9 x - 2)

\int x^{3} 49 - x^{2} d x

\frac{d}{d x} (a (2 x e^{3 x} + e^{3 x} \cdot 3 x^{2}))

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