What is the integral of (6x+15)/(2x+1) ?

The integral of (6x+15)/(2x+1) is 3x+6ln|2x+1|+C

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integral of (6x+15)/(2x+1)

\int \frac{6 x + 15}{2 x + 1} d x

3 x + 6 ln ∣ 2 x + 1 ∣ + C

Solution steps

\int \frac{6 x + 15}{2 x + 1} d x

Long division

\frac{6 x + 15}{2 x + 1} : 3 + \frac{12}{2 x + 1}

= \int 3 + \frac{12}{2 x + 1} d x

Apply the Sum Rule:

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

= \int 3 d x + \int \frac{12}{2 x + 1} d x

\int 3 d x = 3 x

\int \frac{12}{2 x + 1} d x = 6 ln ∣ 2 x + 1 ∣

= 3 x + 6 ln ∣ 2 x + 1 ∣

Add a constant to the solution

= 3 x + 6 ln ∣ 2 x + 1 ∣ + C

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

2 π

\int_{x}^{\infty} e^{- y} d y

\frac{d y}{d x} = \frac{x y + 2 x - y - 2}{x y - 5 x + 6 y - 30}

\int \frac{1}{4 1 + x} d x

What is the integral of (6x+15)/(2x+1) ?
The integral of (6x+15)/(2x+1) is 3x+6ln|2x+1|+C