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

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

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

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

- ln ∣ x + 7 ∣ + x + C

Solution steps

\int \frac{x + 6}{x + 7} d x

\frac{x + 6}{x + 7} = - \frac{1}{x + 7} + 1

= \int - \frac{1}{x + 7} + 1 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 + 7} d x + \int 1 d x

\int \frac{1}{x + 7} d x = ln ∣ x + 7 ∣

\int 1 d x = x

= - ln ∣ x + 7 ∣ + x

Add a constant to the solution

= - ln ∣ x + 7 ∣ + x + C

\frac{1}{s ( s + 1 ) ^{2}}

f (x) = 3 x^{2} - 5, at x = 2

x \to 3 π + lim (cot (x))

\int - 2 x cos (6 x) d x

\frac{\partial}{\partial x} (ln (\frac{x y}{y + z}))

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