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

\frac{\partial}{\partial y} (x^{2} y + z cos (y))

\frac{d}{d x} (sin (- 2 ln (1 - 2 x)))

\frac{x}{x ^{2} - 3}

y^{^{'}} + \frac{1}{x} y = 4 (x + 7)^{2}

4 x (x^{2} - 1)