What is the integral of (2x)/(x^2+100) ?

The integral of (2x)/(x^2+100) is ln|x^2+100|+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+100)

\int \frac{2 x}{x ^{2} + 100} d x

ln x^{2} + 100 + C

Solution steps

\int \frac{2 x}{x ^{2} + 100} 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} + 100} 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} + 100

= 2 \cdot \frac{1}{2} ln x^{2} + 100

Simplify

2 \cdot \frac{1}{2} ln x^{2} + 100 : ln x^{2} + 100

= ln x^{2} + 100

Add a constant to the solution

= ln x^{2} + 100 + C

x \to 2 lim (2 x - 5)

\int \frac{- 6000}{( 3 x + 50 ) ^{2}} d x

\int \frac{2 x - 1}{x ( x ^{2} + 3 x + 2 )} d x

2 \frac{d y}{d t} + y = 0

\frac{d}{d x} (\frac{x - 3}{x - 4})

What is the integral of (2x)/(x^2+100) ?
The integral of (2x)/(x^2+100) is ln|x^2+100|+C