What is the integral of (11x+64)/(x^2+13x+40) ?

The integral of (11x+64)/(x^2+13x+40) is 3ln|x+5|+8ln|x+8|+C

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integral of (11x+64)/(x^2+13x+40)

\int \frac{11 x + 64}{x ^{2} + 13 x + 40} d x

3 ln ∣ x + 5 ∣ + 8 ln ∣ x + 8 ∣ + C

Solution steps

\int \frac{11 x + 64}{x ^{2} + 13 x + 40} d x

Take the partial fraction of

\frac{11 x + 64}{x ^{2} + 13 x + 40} : \frac{3}{x + 5} + \frac{8}{x + 8}

= \int \frac{3}{x + 5} + \frac{8}{x + 8} 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{3}{x + 5} d x + \int \frac{8}{x + 8} d x

\int \frac{3}{x + 5} d x = 3 ln ∣ x + 5 ∣

\int \frac{8}{x + 8} d x = 8 ln ∣ x + 8 ∣

= 3 ln ∣ x + 5 ∣ + 8 ln ∣ x + 8 ∣

Add a constant to the solution

= 3 ln ∣ x + 5 ∣ + 8 ln ∣ x + 8 ∣ + C

x \to 0 lim (\frac{( x ^{2} )}{e - 1})

\frac{\partial}{\partial x} (1 - x^{2} - x - 2 y^{2} + y)

ln (2) + ln (x)

y = \frac{e ^{6 x}}{e ^{6 x} + 3}

\frac{\partial}{\partial x} (e^{- 3 y} cos (π x))

What is the integral of (11x+64)/(x^2+13x+40) ?
The integral of (11x+64)/(x^2+13x+40) is 3ln|x+5|+8ln|x+8|+C