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Popular >

integral of 1/(2-8x)

Solution

\int \frac{1}{2 - 8 x} d x

Solution

- \frac{1}{8} ln ∣ 2 - 8 x ∣ + C

Solution steps

\int \frac{1}{2 - 8 x} d x

Apply u-substitution

: \int - \frac{1}{8 u} d u

= \int - \frac{1}{8 u} d u

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{8} ln ∣ u ∣

Substitute back

u = 2 - 8 x

= - \frac{1}{8} ln ∣ 2 - 8 x ∣

Add a constant to the solution

= - \frac{1}{8} ln ∣ 2 - 8 x ∣ + C

Popular Examples

limit as x approaches 2 of-((1/2)/(x-2))

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

derivative of 1/(16x^2)

\frac{d}{d x} (\frac{1}{16 x ^{2}})

derivative of sqrt(3+6x)

\frac{d}{d x} (3 + 6 x)

integral from 0 to 9 of sqrt(x)-1/3 x

\int_{0}^{9} x - \frac{1}{3} x d x

\frac{d y}{d t} = - 2 y

Frequently Asked Questions (FAQ)

What is the integral of 1/(2-8x) ?
The integral of 1/(2-8x) is -1/8 ln|2-8x|+C