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

\frac{1}{2 s ^{2} + 2 s + 1}

arctan (x^{\frac{1}{2}})

\int (x + 3) (x^{2} + 6 x - 7) d x

\frac{\partial}{\partial x} (x^{2} + z^{2})

\frac{1}{x ^{2} ( x ^{2} + 4 x + 13 )}

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