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

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

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

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

2 (x + \frac{1}{x}) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int 1 - \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

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

\int 1 d x = x

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

= 2 (x - (- \frac{1}{x}))

Simplify

= 2 (x + \frac{1}{x})

Add a constant to the solution

= 2 (x + \frac{1}{x}) + C

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x \to 0 lim (tan (2 x))

\frac{d}{d x} (3 x + 9)

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