What is the integral of (2x)/(x^2-9) ?

The integral of (2x)/(x^2-9) is ln|x^2-9|+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^2-9)

\int \frac{2 x}{x ^{2} - 9} d x

ln x^{2} - 9 + C

Solution steps

\int \frac{2 x}{x ^{2} - 9} 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} - 9} 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} - 9

= 2 \cdot \frac{1}{2} ln x^{2} - 9

Simplify

2 \cdot \frac{1}{2} ln x^{2} - 9 : ln x^{2} - 9

= ln x^{2} - 9

Add a constant to the solution

= ln x^{2} - 9 + C

e^{- 2 s}

\frac{d}{d x} (- 4 e^{- 2 x})

x \to 0 + lim (\frac{1}{4 x})

\frac{( tan ( x ) - 1 )}{sec ( x )}

ln (2 - e^{x})

What is the integral of (2x)/(x^2-9) ?
The integral of (2x)/(x^2-9) is ln|x^2-9|+C