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

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

Popular >

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

\int \frac{( x + 2 )}{x ^{2} + 4 x} d x

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

Solution steps

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

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

Add a constant to the solution

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

y = arcsin (6 x + 1)

\int \frac{2 x ^{2} + x - 8}{x ^{3} + 4 x} d x

\frac{\partial}{\partial y} (\frac{x ^{2} - y ^{2}}{z ^{2}})

\frac{x}{x + \frac{d}{x}}

f (x) = (2 x^{5} - 3)^{8}

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