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

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

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integral of (x^{-1})/(-1)

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

- ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int x^{- 1} d x = ln (∣ x ∣)

= - ln ∣ x ∣

Add a constant to the solution

= - ln ∣ x ∣ + C

\int \frac{( a ^{x} ln ( a ) )}{( a ^{x} + 1 )} d x

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\int \frac{( e ^{x} e ^{x} - 1 )}{e ^{x} + 8} d x

\int \frac{1}{( y )} d y

\int 0.09 e^{0.04 x} d x

What is the integral of (x^{-1})/(-1) ?
The integral of (x^{-1})/(-1) is -ln|x|+C