What is the integral of (13)/((x-7)(x+6)) ?

The integral of (13)/((x-7)(x+6)) is ln|x-7|-ln|x+6|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (13)/((x-7)(x+6))

\int \frac{13}{( x - 7 ) ( x + 6 )} d x

ln ∣ x - 7 ∣ - ln ∣ x + 6 ∣ + C

Solution steps

\int \frac{13}{( x - 7 ) ( x + 6 )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 13 \cdot \int \frac{1}{( x - 7 ) ( x + 6 )} d x

Take the partial fraction of

\frac{1}{( x - 7 ) ( x + 6 )} : \frac{1}{13 ( x - 7 )} - \frac{1}{13 ( x + 6 )}

= 13 \cdot \int \frac{1}{13 ( x - 7 )} - \frac{1}{13 ( 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

= 13 (\int \frac{1}{13 ( x - 7 )} d x - \int \frac{1}{13 ( x + 6 )} d x)

\int \frac{1}{13 ( x - 7 )} d x = \frac{1}{13} ln ∣ x - 7 ∣

\int \frac{1}{13 ( x + 6 )} d x = \frac{1}{13} ln ∣ x + 6 ∣

= 13 (\frac{1}{13} ln ∣ x - 7 ∣ - \frac{1}{13} ln ∣ x + 6 ∣)

Simplify

13 (\frac{1}{13} ln ∣ x - 7 ∣ - \frac{1}{13} ln ∣ x + 6 ∣) : ln ∣ x - 7 ∣ - ln ∣ x + 6 ∣

= ln ∣ x - 7 ∣ - ln ∣ x + 6 ∣

Add a constant to the solution

= ln ∣ x - 7 ∣ - ln ∣ x + 6 ∣ + C

\int e^{- \frac{x}{y}} d x

\frac{d}{d x} (a x a + x)

f (x) = tan (x^{2})

x \to - 4 lim (\frac{x ^{2}}{4 - x})

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{- x}, y (0) = 4, y^{^{'}} (0) = - 1

What is the integral of (13)/((x-7)(x+6)) ?
The integral of (13)/((x-7)(x+6)) is ln|x-7|-ln|x+6|+C