What is the integral of (x+4)/(x^3) ?

The integral of (x+4)/(x^3) is -1/x-2/(x^2)+C

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integral of (x+4)/(x^3)

\int \frac{x + 4}{x ^{3}} d x

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

Solution steps

\int \frac{x + 4}{x ^{3}} d x

Expand

\frac{x + 4}{x ^{3}} : \frac{1}{x ^{2}} + \frac{4}{x ^{3}}

= \int \frac{1}{x ^{2}} + \frac{4}{x ^{3}} 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 ^{2}} d x + \int \frac{4}{x ^{3}} d x

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

\int \frac{4}{x ^{3}} d x = - \frac{2}{x ^{2}}

= - \frac{1}{x} - \frac{2}{x ^{2}}

Add a constant to the solution

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

f (x) = 2 x - 1

\int (4 x^{7} - 3 cos (x)) d x

f (x) = 4 x + 8

y^{^{'}} = - x - y

x \to 1 + lim (4 x - 1)

What is the integral of (x+4)/(x^3) ?
The integral of (x+4)/(x^3) is -1/x-2/(x^2)+C