What is the integral of ((2x+5))/(x^2+5x+6) ?

The integral of ((2x+5))/(x^2+5x+6) is ln|x^2+5x+6|+C

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integral of ((2x+5))/(x^2+5x+6)

\int \frac{( 2 x + 5 )}{x ^{2} + 5 x + 6} d x

ln x^{2} + 5 x + 6 + C

Solution steps

\int \frac{2 x + 5}{x ^{2} + 5 x + 6} d x

Apply u-substitution

= \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} + 5 x + 6

= ln x^{2} + 5 x + 6

Add a constant to the solution

= ln x^{2} + 5 x + 6 + C

\int \frac{21 x ^{2}}{x ^{2} - 4} d x

\frac{d}{d x} (\frac{3 x ^{5} + 8}{x ^{3}})

\int 2 x ln (2 x) d x

y^{^{''}} - 6 y^{^{'}} + 10 y = 0

d er i v a t i v e C (x) = \frac{4 x + 50}{x + 2}

What is the integral of ((2x+5))/(x^2+5x+6) ?
The integral of ((2x+5))/(x^2+5x+6) is ln|x^2+5x+6|+C