What is the integral of (x+2)/(x^3) ?

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

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integral of (x+2)/(x^3)

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

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (2 x e^{x^{2}})

\int (sec^{2} (π x) - x) d x

\frac{\partial}{\partial x} ((\frac{y x}{z w})^{\frac{1}{2}})

\frac{d}{d x} (\frac{4 - x e ^{x}}{x + e ^{x}})

n = 1 \sum \infty \frac{cos ( nπ )}{n ^{2}}

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