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Popular >

integral of x/(x+2)

Solution

\int \frac{x}{x + 2} d x

Solution

x + 2 - 2 ln ∣ x + 2 ∣ + C

Solution steps

\int \frac{x}{x + 2} d x

Apply u-substitution

: \int \frac{u - 2}{u} d u

= \int \frac{u - 2}{u} d u

Expand

\frac{u - 2}{u} : 1 - \frac{2}{u}

= \int 1 - \frac{2}{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{2}{u} d u

\int 1 d u = u

\int \frac{2}{u} d u = 2 ln ∣ u ∣

= u - 2 ln ∣ u ∣

Substitute back

u = x + 2

= x + 2 - 2 ln ∣ x + 2 ∣

Add a constant to the solution

= x + 2 - 2 ln ∣ x + 2 ∣ + C

Popular Examples

integral of 2cos^3(x)

\int 2 cos^{3} (x) d x

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

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

derivative of (x^3/9+3/(4x))

\frac{d}{d x} (\frac{x ^{3}}{9} + \frac{3}{4 x})

area 9(x^3-x),0 area

9 (x^{3} - x), 0

laplacetransform t^2e^{5t}laplace transform

t^{2} e^{5 t}

Frequently Asked Questions (FAQ)

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