What is the integral of-5/x ?

The integral of-5/x is -5ln|x|+C

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integral of-5/x

\int - \frac{5}{x} d x

- 5 ln ∣ x ∣ + C

Solution steps

\int - \frac{5}{x} d x

Take the constant out:

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

= - 5 \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - 5 ln ∣ x ∣

Add a constant to the solution

= - 5 ln ∣ x ∣ + C

\int - 6 x^{- 1} d x

y^{^{''}} + y^{^{'}} = 6 x

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

f (x) = \frac{x}{1 - ln ( x - 2 )}

t \to 1 lim ((t^{3} + 3)^{4})