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^{^{'}} - \frac{3}{2} y = 3 + 2 e^{t}

\frac{\partial}{\partial x} (x^{2} - 4 x y + 4 y^{2} + 2)

x, 1, \frac{x ^{2}}{4}

y = \frac{cos ( x )}{x ^{3}}

y = 600 - \frac{x ^{2}}{121}