What is the integral of (2x)/(x^2+6) ?

The integral of (2x)/(x^2+6) is ln|x^2+6|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x)/(x^2+6)

\int \frac{2 x}{x ^{2} + 6} d x

ln x^{2} + 6 + C

Solution steps

\int \frac{2 x}{x ^{2} + 6} 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} + 6} 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} + 6

= 2 \cdot \frac{1}{2} ln x^{2} + 6

Simplify

2 \cdot \frac{1}{2} ln x^{2} + 6 : ln x^{2} + 6

= ln x^{2} + 6

Add a constant to the solution

= ln x^{2} + 6 + C

\frac{d}{d x} (\frac{x}{2} + 1)

5 y^{^{'}} = y^{2}

\int sin (3 x) sin^{2} (4 x) d x

\frac{\partial}{\partial x} (ln (9 x^{2} + 5 y^{2}))

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

What is the integral of (2x)/(x^2+6) ?
The integral of (2x)/(x^2+6) is ln|x^2+6|+C