What is the integral of (2x+3)/(x+2) ?

The integral of (2x+3)/(x+2) is 2(x+2)-ln|x+2|+C

Popular >

integral of (2x+3)/(x+2)

\int \frac{2 x + 3}{x + 2} d x

2 (x + 2) - ln ∣ x + 2 ∣ + C

Solution steps

\int \frac{2 x + 3}{x + 2} d x

Apply u-substitution

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

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

Expand

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

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

\int 2 d u = 2 u

\int \frac{1}{u} d u = ln ∣ u ∣

= 2 u - ln ∣ u ∣

Substitute back

u = x + 2

= 2 (x + 2) - ln ∣ x + 2 ∣

Add a constant to the solution

= 2 (x + 2) - ln ∣ x + 2 ∣ + C

\frac{d}{d t} (a t - tanh (a t))

\int_{0}^{6} - 2 x d x

\frac{d}{d x} (\frac{2}{9} x^{3} + 3 x + cos (x) + 1)

\frac{\partial}{\partial x} (arcsin (2 x yz))

\int \frac{25}{x x} d x

What is the integral of (2x+3)/(x+2) ?
The integral of (2x+3)/(x+2) is 2(x+2)-ln|x+2|+C