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

\int e^{3 x} sin (6 x) d x

250000 + 15000 x - 0.3 x^{3}

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

ln (5 x + ln (3 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