What is the integral of 1/(x^2+9x+20) ?

The integral of 1/(x^2+9x+20) is ln|x+4|-ln|x+5|+C

Popular >

integral of 1/(x^2+9x+20)

\int \frac{1}{x ^{2} + 9 x + 20} d x

ln ∣ x + 4 ∣ - ln ∣ x + 5 ∣ + C

Solution steps

\int \frac{1}{x ^{2} + 9 x + 20} d x

Take the partial fraction of

\frac{1}{x ^{2} + 9 x + 20} : \frac{1}{x + 4} - \frac{1}{x + 5}

= \int \frac{1}{x + 4} - \frac{1}{x + 5} 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 + 4} d x - \int \frac{1}{x + 5} d x

\int \frac{1}{x + 4} d x = ln ∣ x + 4 ∣

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

= ln ∣ x + 4 ∣ - ln ∣ x + 5 ∣

Add a constant to the solution

= ln ∣ x + 4 ∣ - ln ∣ x + 5 ∣ + C

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

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

x^{2 e^{- 42}}

\frac{9}{x}, 2 x, \frac{1}{2} x

\int 4 \frac{cos ( x ) + sin ( 2 x )}{sin ( x )} d x

What is the integral of 1/(x^2+9x+20) ?
The integral of 1/(x^2+9x+20) is ln|x+4|-ln|x+5|+C