What is the integral of (2x+3)/(x+1) ?

The integral of (2x+3)/(x+1) is 2(x+1)+ln|x+1|+C

Popular >

integral of (2x+3)/(x+1)

\int \frac{2 x + 3}{x + 1} d x

2 (x + 1) + ln ∣ x + 1 ∣ + C

Solution steps

\int \frac{2 x + 3}{x + 1} 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 + 1

= 2 (x + 1) + ln ∣ x + 1 ∣

Add a constant to the solution

= 2 (x + 1) + ln ∣ x + 1 ∣ + C

x^{3} - 8 x^{2} + 19 x - 12

\int_{5}^{10} (3 x + 3) d x

\frac{\partial}{\partial y} (x^{3} - y^{2} + 2 x y)

f (x) = \frac{x ^{2}}{3 + x}

What is the integral of (2x+3)/(x+1) ?
The integral of (2x+3)/(x+1) is 2(x+1)+ln|x+1|+C