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

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

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integral of 2/(1+x^2)

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

2 arctan (x) + C

Solution steps

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

Use the common integral:

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

= 2 arctan (x)

Add a constant to the solution

= 2 arctan (x) + C

x \to - \infty lim (\frac{- 1}{x})

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\frac{1}{x - 1}, x = 7