What is the integral of (2x)/(3+x^2) ?

The integral of (2x)/(3+x^2) is ln|3+x^2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x)/(3+x^2)

\int \frac{2 x}{3 + x ^{2}} d x

ln 3 + x^{2} + C

Solution steps

\int \frac{2 x}{3 + x ^{2}} 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}{3 + x ^{2}} 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 = 3 + x^{2}

= 2 \cdot \frac{1}{2} ln 3 + x^{2}

Simplify

2 \cdot \frac{1}{2} ln 3 + x^{2} : ln 3 + x^{2}

= ln 3 + x^{2}

Add a constant to the solution

= ln 3 + x^{2} + C

\frac{d y}{d t} = \frac{y t - y}{( r ^{2} + 1 )}

\int 14 cot (7 x) csc^{2} (7 x) d x

i = 1 \sum \infty i^{2}

\int \frac{t ^{5}}{t ^{2} + 7} d t

\int sec^{2} (3 x) tan (3 x) d x

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