Question

evaluate.

int \frac { 9 } { x } d x

int \frac { 9 } { x } d x = square
(use parentheses to clearly denote the argument of each function.)

Explanation:

Step1: Use the constant multiple rule

The constant multiple rule of integration states that \(\int kf(x)dx = k\int f(x)dx\) where \(k\) is a constant. Here \(k = 9\) and \(f(x)=\frac{1}{x}\). So, \(\int\frac{9}{x}dx=9\int\frac{1}{x}dx\).

Step2: Integrate \(\frac{1}{x}\)

We know that the integral of \(\frac{1}{x}\) with respect to \(x\) is \(\ln|x|\) (plus a constant of integration \(C\)). So, \(9\int\frac{1}{x}dx = 9\ln|x|+C\).

Answer:

\(9\ln|x| + C\)