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

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

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

integral

\frac{( x + 2 )}{( x ^{2} + x ^{2} )}

\frac{1}{2} ln ∣ x ∣ - \frac{1}{x} + C

Solution steps

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

Expand

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

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

\int \frac{1}{2 x} d x = \frac{1}{2} ln ∣ x ∣

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

= \frac{1}{2} ln ∣ x ∣ - \frac{1}{x}

Add a constant to the solution

= \frac{1}{2} ln ∣ x ∣ - \frac{1}{x} + C

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