What is the integral of 1/(Ca) ?

The integral of 1/(Ca) is 1/C ln|a|+C

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integral of 1/(Ca)

\int \frac{1}{C a} d a

\frac{1}{C} ln ∣ a ∣ + C

Solution steps

\int \frac{1}{C a} d a

Take the constant out:

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

= \frac{1}{C} \cdot \int \frac{1}{a} d a

Use the common integral:

\int \frac{1}{a} d a = ln (∣ a ∣)

= \frac{1}{C} ln ∣ a ∣

Add a constant to the solution

= \frac{1}{C} ln ∣ a ∣ + C