What is the integral of 1/(xy) ?

The integral of 1/(xy) is 1/y ln|x|+C

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integral of 1/(xy)

integral

\frac{1}{x y}

\frac{1}{y} ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{y} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{y} ln ∣ x ∣ + C

lo g_{10} (x) + 1

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

\frac{1}{2} - 3 cos^{2} (x)

\frac{1}{( x + x ^{2} )}

\frac{2}{t}