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

The integral of (2x)/(x^2+3) is ln|x^2+3|+C

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integral of (2x)/(x^2+3)

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

ln x^{2} + 3 + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{2 u} d u

= 2 \cdot \int \frac{1}{2 u} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 \cdot \frac{1}{2} ln ∣ u ∣

Substitute back

u = x^{2} + 3

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

Simplify

2 \cdot \frac{1}{2} ln x^{2} + 3 : ln x^{2} + 3

= ln x^{2} + 3

Add a constant to the solution

= ln x^{2} + 3 + C

x \to 0 lim (x^{x^{4}})

\frac{d x}{d t} = 0.8 x - 0.004 x^{2}

x \to 0 lim (\frac{( 1 + x ) ^{n} - 1}{x})

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

\int_{0}^{\infty} e^{5 - 2 x} d x

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