What is the integral of (-4)/x ?

The integral of (-4)/x is -4ln|x|+C

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integral of (-4)/x

\int \frac{- 4}{x} d x

- 4 ln ∣ x ∣ + C

Solution steps

\int \frac{- 4}{x} d x

Take the constant out:

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

= - 4 \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - 4 ln ∣ x ∣

Add a constant to the solution

= - 4 ln ∣ x ∣ + C

\int_{0}^{2} (x - 1) e^{(x - 1)^{2}} d x

f (x) = (2 x - 5)^{3}, at x = 1

\int e^{8 x} cos (3 x) d x

f (x) = 6 tan (x), at x = \frac{π}{3}

\frac{\partial}{\partial x} (2 x - 1)