What is the integral of-8/x ?

The integral of-8/x is -8ln|x|+C

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integral of-8/x

\int - \frac{8}{x} d x

- 8 ln ∣ x ∣ + C

Solution steps

\int - \frac{8}{x} d x

Take the constant out:

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

= - 8 \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - 8 ln ∣ x ∣

Add a constant to the solution

= - 8 ln ∣ x ∣ + C

\int \frac{2 x ^{2} + 13 x + 18}{x ^{3} + 6 x ^{2} + 9 x} d x

y^{^{''}} - 5 y^{^{'}} + 6 y = e^{2 x}

\int 9 x^{2} - 4 x d x

\frac{\partial}{\partial x} (1 + ln (x))

s (t) = \frac{t ^{2} + 40 t}{5}