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

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

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integral of 3/(x^2+3)

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integral Substitution

= 3 \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

= 3 \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)

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

Substitute back

u = \frac{x}{3}

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

Simplify

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

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

Add a constant to the solution

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

\frac{d y}{d x} = x^{4} - 1

g (x) = 1 + 6 x + 3 x^{2}

\int \frac{x}{x ^{2} + 4 x + 20} d x

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

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