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

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

Popular >

integral of (x-3)/(x^3)

\int \frac{x - 3}{x ^{3}} d x

- \frac{1}{x} + \frac{3}{2 x ^{2}} + C

Solution steps

\int \frac{x - 3}{x ^{3}} d x

Expand

\frac{x - 3}{x ^{3}} : \frac{1}{x ^{2}} - \frac{3}{x ^{3}}

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

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

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

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

Simplify

= - \frac{1}{x} + \frac{3}{2 x ^{2}}

Add a constant to the solution

= - \frac{1}{x} + \frac{3}{2 x ^{2}} + C

\frac{d}{d x} (16 - 5 x^{2})

x \to 2 - lim (sin (\frac{1}{x - 2}))

x \to 2 lim (x^{2} + 2)

\frac{d y}{d x} = 18 - y

(1 + x) e^{2 x}

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