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

The integral of 2/(x^2+3) is 2/(sqrt(3))arctan(x/(sqrt(3)))+C

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integral of 2/(x^2+3)

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

\frac{2}{3} arctan (\frac{x}{3}) + C

Solution steps

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

Apply Integral Substitution

= 2 \cdot \int \frac{1}{3 ( u ^{2} + 1 )} d u

Take the constant out:

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

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

Use the common integral:

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

= 2 \cdot \frac{1}{3} arctan (u)

Substitute back

u = \frac{x}{3}

= 2 \cdot \frac{1}{3} arctan (\frac{x}{3})

Simplify

2 \cdot \frac{1}{3} arctan (\frac{x}{3}) : \frac{2}{3} arctan (\frac{x}{3})

= \frac{2}{3} arctan (\frac{x}{3})

Add a constant to the solution

= \frac{2}{3} arctan (\frac{x}{3}) + C

(x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}}) d x + (x^{3} y^{2}) d y = 0

\frac{d}{d x} (sin^{2} (x) - cos^{2} (x))

ln (2 x + 1)

x \to 5 lim (\frac{3}{x - 5})

\frac{d}{d x} (∣ x ∣^{x})

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