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Popular Calculus >

integral of x/(x+4)

Solution

\int \frac{x}{x + 4} d x

Solution

x + 4 - 4 ln ∣ x + 4 ∣ + C

Solution steps

\int \frac{x}{x + 4} d x

Apply u-substitution

= \int \frac{u - 4}{u} d u

Expand

\frac{u - 4}{u} : 1 - \frac{4}{u}

= \int 1 - \frac{4}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d u - \int \frac{4}{u} d u

\int 1 d u = u

\int \frac{4}{u} d u = 4 ln ∣ u ∣

= u - 4 ln ∣ u ∣

Substitute back

u = x + 4

= x + 4 - 4 ln ∣ x + 4 ∣

Add a constant to the solution

= x + 4 - 4 ln ∣ x + 4 ∣ + C

Graph

Popular Examples

tangent of f(x)=(2x)/(x^2-7),(3,3)

(x^2+1)y^'+9x(y-1)=0

integral of (cos(x))^4

derivative of f(x)=(x-3)/(x+4)

laplacetransform t^2-4t+4

Frequently Asked Questions (FAQ)

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