What is the integral of (6/x) ?

The integral of (6/x) is 6ln|x|+C

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integral of (6/x)

\int (\frac{6}{x}) d x

6 ln ∣ x ∣ + C

Solution steps

\int \frac{6}{x} d x

Take the constant out:

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

= 6 \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 6 ln ∣ x ∣

Add a constant to the solution

= 6 ln ∣ x ∣ + C

\int 2 x + 6 e^{x} d x

\frac{d}{d x} (\frac{x}{x ^{2}})

y^{^{''}} - 2 y^{^{'}} + y = e^{x} ln (x)

\frac{d}{d x} (arcsin (\frac{x}{4}))

\frac{d}{d x} (tan^{4} (3 x))