What is the integral of x/(16+x^2) ?

The integral of x/(16+x^2) is 1/2 ln|16+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 x/(16+x^2)

\int \frac{x}{16 + x ^{2}} d x

\frac{1}{2} ln 16 + x^{2} + C

Solution steps

\int \frac{x}{16 + x ^{2}} d x

Apply u-substitution

: \int \frac{1}{2 u} d u

= \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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = 16 + x^{2}

= \frac{1}{2} ln 16 + x^{2}

Add a constant to the solution

= \frac{1}{2} ln 16 + x^{2} + C

\int \frac{2}{9 + 4 x ^{2}} d x

\int \frac{1}{9 x - 1} d x

\int \frac{x - 2}{1 - x ^{2}} d x

\int (1 - x^{2} - 3 x^{5}) d x

\int e^{u + 1} d u

What is the integral of x/(16+x^2) ?
The integral of x/(16+x^2) is 1/2 ln|16+x^2|+C