What is the integral of ((x+1))/(x^2+2x+8) ?

The integral of ((x+1))/(x^2+2x+8) is 1/2 ln|x^2+2x+8|+C

Popular >

integral of ((x+1))/(x^2+2x+8)

\int \frac{( x + 1 )}{x ^{2} + 2 x + 8} d x

\frac{1}{2} ln x^{2} + 2 x + 8 + C

Solution steps

\int \frac{x + 1}{x ^{2} + 2 x + 8} 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} + 2 x + 8

= \frac{1}{2} ln x^{2} + 2 x + 8

Add a constant to the solution

= \frac{1}{2} ln x^{2} + 2 x + 8 + C

\int x^{3} e^{x^{4 + 5}} d x

\frac{4}{s \cdot ( s ^{2} - 4 s + 5 )}

\int_{0}^{1} \frac{1}{x ^{2} + 2 x + 1} d x

\frac{d}{d x} (6 x - 7 e^{6 x})

x \to 0 lim (\frac{∣ 0 ∣}{0})

What is the integral of ((x+1))/(x^2+2x+8) ?
The integral of ((x+1))/(x^2+2x+8) is 1/2 ln|x^2+2x+8|+C