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

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

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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}})

Simplify

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

Add a constant to the solution

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

f (y) = 2 e^{y}

x \to - 4 lim (\frac{\frac{4}{x} + 1}{x + 4})

\int_{0}^{1} 1 + (- 2 x)^{2} d x

f (x) = x^{2} + 5, (3, 14)

\frac{x}{4} - \frac{4}{x}

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