What is the integral of (21x-12)/x ?

The integral of (21x-12)/x is 21x-12ln|x|+C

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integral of (21x-12)/x

\int \frac{21 x - 12}{x} d x

21 x - 12 ln ∣ x ∣ + C

Solution steps

\int \frac{21 x - 12}{x} d x

Expand

\frac{21 x - 12}{x} : 21 - \frac{12}{x}

= \int 21 - \frac{12}{x} 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 21 d x - \int \frac{12}{x} d x

\int 21 d x = 21 x

\int \frac{12}{x} d x = 12 ln ∣ x ∣

= 21 x - 12 ln ∣ x ∣

Add a constant to the solution

= 21 x - 12 ln ∣ x ∣ + C

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What is the integral of (21x-12)/x ?
The integral of (21x-12)/x is 21x-12ln|x|+C