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

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

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

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

ln x^{2} + 3 x + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x^{2} + 3 x

= ln x^{2} + 3 x

Add a constant to the solution

= ln x^{2} + 3 x + C

\int (4 w - 1)^{3} d w

\frac{\partial}{\partial x} (e^{(x + y)})

\frac{\partial}{\partial x} (10 x y - 16 x)

\frac{d}{d x} (0.5 x)

x \to - 3 - lim (g (x))

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