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

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

Popular >

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

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

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

Solution steps

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

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

Add a constant to the solution

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

\int \frac{6 x ^{3} - 12 x ^{2} + 8}{x ^{2} - 2 x} d x

\int_{0}^{1} ((x + 2) (x - 3)) d x

e^{x + 2}

(4 + x) y^{^{'}} = 7 y

x \to 0 lim (\frac{e ^{- 8 x} - 1}{x})

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