What is the integral of (2x)/(x^2+4) ?

The integral of (2x)/(x^2+4) is ln|x^2+4|+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+4)

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

ln x^{2} + 4 + C

Solution steps

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

= 2 \cdot \frac{1}{2} ln x^{2} + 4

Simplify

2 \cdot \frac{1}{2} ln x^{2} + 4 : ln x^{2} + 4

= ln x^{2} + 4

Add a constant to the solution

= ln x^{2} + 4 + C

\frac{d}{d x} (sin ((π x)^{3}))

(2 x + 1)^{4}

x \to \infty lim (lo g_{2} (\frac{( x + 2 )}{( 2 \cdot x + 1 )}))

\int_{1}^{8} x - 1 d x

x^{2} x^{3} + 1

What is the integral of (2x)/(x^2+4) ?
The integral of (2x)/(x^2+4) is ln|x^2+4|+C