What is the integral of 1/(4x)-10 ?

The integral of 1/(4x)-10 is 1/4 ln|x|-10x+C

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integral of 1/(4x)-10

\int \frac{1}{4 x} - 10 d x

\frac{1}{4} ln ∣ x ∣ - 10 x + C

Solution steps

\int \frac{1}{4 x} - 10 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}{4 x} d x - \int 10 d x

\int \frac{1}{4 x} d x = \frac{1}{4} ln ∣ x ∣

\int 10 d x = 10 x

= \frac{1}{4} ln ∣ x ∣ - 10 x

Add a constant to the solution

= \frac{1}{4} ln ∣ x ∣ - 10 x + C

What is the integral of 1/(4x)-10 ?
The integral of 1/(4x)-10 is 1/4 ln|x|-10x+C