What is the integral of 1/(x^2+11x+30) ?

The integral of 1/(x^2+11x+30) is ln|x+5|-ln|x+6|+C

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integral of 1/(x^2+11x+30)

\int \frac{1}{x ^{2} + 11 x + 30} d x

ln ∣ x + 5 ∣ - ln ∣ x + 6 ∣ + C

Solution steps

\int \frac{1}{x ^{2} + 11 x + 30} d x

Take the partial fraction of

\frac{1}{x ^{2} + 11 x + 30} : \frac{1}{x + 5} - \frac{1}{x + 6}

= \int \frac{1}{x + 5} - \frac{1}{x + 6} 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 \frac{1}{x + 5} d x - \int \frac{1}{x + 6} d x

\int \frac{1}{x + 5} d x = ln ∣ x + 5 ∣

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

= ln ∣ x + 5 ∣ - ln ∣ x + 6 ∣

Add a constant to the solution

= ln ∣ x + 5 ∣ - ln ∣ x + 6 ∣ + C

\int x \cdot e^{- a x} d x

\int \frac{x ^{2}}{( x ^{2} + 4 x + 5 ) ^{2}} d x

\frac{d}{d x} (\frac{1}{2 x + 5})

\int \frac{cos ^{2} ( x )}{1 - sin ( x )} d x

x \to 2 lim (9 x)

What is the integral of 1/(x^2+11x+30) ?
The integral of 1/(x^2+11x+30) is ln|x+5|-ln|x+6|+C