What is the integral of (1+1/x)(1/(x^2)) ?

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

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integral of (1+1/x)(1/(x^2))

\int (1 + \frac{1}{x}) (\frac{1}{x ^{2}}) d x

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

Solution steps

\int (1 + \frac{1}{x}) \frac{1}{x ^{2}} d x

Simplify

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

= \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

y^{^{'}} = 9.8 - \frac{k y}{7}, y (0) = 94

e^{4 s i n (x)}

\frac{d}{d x} ((1 + 2 cos (x)) sin (x))

\frac{\partial}{\partial y} (sin (y) cos (x))

n = 0 \sum \infty \frac{2 ^{n}}{n ^{2}}

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