What is the integral of (-1)/x ?

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

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integral of (-1)/x

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

- ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - ln ∣ x ∣

Add a constant to the solution

= - ln ∣ x ∣ + C

y (x + 7) + y^{^{'}} = 0

\frac{d}{d x} (tan (5 x + 2))

\frac{d}{d x} (x^{3} \cdot e^{- x})

\frac{d}{d x} (x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 9)

x^{4} + x y^{2} = 5, (1, 2)