What is the integral of (x+4)/(x^8) ?

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

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integral of (x+4)/(x^8)

\int \frac{x + 4}{x ^{8}} d x

- \frac{1}{6 x ^{6}} - \frac{4}{7 x ^{7}} + C

Solution steps

\int \frac{x + 4}{x ^{8}} d x

Expand

\frac{x + 4}{x ^{8}} : \frac{1}{x ^{7}} + \frac{4}{x ^{8}}

= \int \frac{1}{x ^{7}} + \frac{4}{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 \frac{1}{x ^{7}} d x + \int \frac{4}{x ^{8}} d x

\int \frac{1}{x ^{7}} d x = - \frac{1}{6 x ^{6}}

\int \frac{4}{x ^{8}} d x = - \frac{4}{7 x ^{7}}

= - \frac{1}{6 x ^{6}} - \frac{4}{7 x ^{7}}

Add a constant to the solution

= - \frac{1}{6 x ^{6}} - \frac{4}{7 x ^{7}} + C

\frac{d}{d x} (7 x e^{- x})

\frac{d}{d x} (\frac{( 4 x ^{2} + 4 x + 1 )}{( 2 x + 1 )})

x \to 0 lim (\frac{1}{e ^{2 x} - 1})

\int x cos (5 x^{2}) d x

x \to 2 lim (\frac{4 x}{x - 4})

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