What is the integral of (x+2)/(x^2+4x+7) ?

The integral of (x+2)/(x^2+4x+7) is 1/2 ln|x^2+4x+7|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+2)/(x^2+4x+7)

\int \frac{x + 2}{x ^{2} + 4 x + 7} d x

\frac{1}{2} ln x^{2} + 4 x + 7 + C

Solution steps

\int \frac{x + 2}{x ^{2} + 4 x + 7} 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 = x^{2} + 4 x + 7

= \frac{1}{2} ln x^{2} + 4 x + 7

Add a constant to the solution

= \frac{1}{2} ln x^{2} + 4 x + 7 + C

\int \frac{1 + 4 x ^{2}}{x} d x

\int \frac{- 2}{7 x ^{4}} d x

\int e^{- x^{8}} x^{7} d x

\int 2 x sin (6 x) d x

\int (sin^{2} (\frac{x}{2})) d x

What is the integral of (x+2)/(x^2+4x+7) ?
The integral of (x+2)/(x^2+4x+7) is 1/2 ln|x^2+4x+7|+C