What is the integral of 1/(ax) ?

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

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integral of 1/(ax)

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

\frac{1}{a} ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{a} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{a} ln ∣ x ∣ + C

\frac{d}{d x} (z + y^{3} + y + x)

x \to - 2 lim (x^{2} - 4 x + 10)

\int \frac{1}{( x ^{2} - 2 ) ^{2}} d x

\frac{\partial}{\partial x} (2 x e^{2 y})

x^{^{'}} = 2 (x + 1)