What is the integral of (-2x^{-1}) ?

The integral of (-2x^{-1}) is -2ln|x|+C

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integral of (-2x^{-1})

\int (- 2 x^{- 1}) d x

- 2 ln ∣ x ∣ + C

Solution steps

\int - 2 x^{- 1} d x

Take the constant out:

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

= - 2 \cdot \int x^{- 1} d x

Use the common integral:

\int x^{- 1} d x = ln (∣ x ∣)

= - 2 ln ∣ x ∣

Add a constant to the solution

= - 2 ln ∣ x ∣ + C

cos (2 \cdot t)

\frac{d y}{d x} = (x - 3) e^{- 2 y}, y (3) = ln (3)

y = lo g_{2} (lo g_{2} (x))

x \to 1 lim (- \frac{x ^{2}}{2} + 2 x + 4)

\frac{d}{d x} (\frac{x ^{3}}{3} - 10 x^{2} + 100 x)