What is the integral of (x+1)/(x^3) ?

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

Popular >

integral of (x+1)/(x^3)

\int \frac{x + 1}{x ^{3}} d x

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

Solution steps

\int \frac{x + 1}{x ^{3}} d x

Expand

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

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (x e^{8 x})

n = 0 \sum \infty 4^{2 n + 1}

\frac{\partial}{\partial x} (∣ x - y ∣)

\frac{d}{d x} (ln^{4} (\frac{( x ^{2} - 1 ) ^{3}}{x ^{2} - 1}))

\int sin (x) sin (cos (x)) d x

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