What is the integral of 1/((7-8x)) ?

The integral of 1/((7-8x)) is -1/8 ln|7-8x|+C

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integral of 1/((7-8x))

\int \frac{1}{( 7 - 8 x )} d x

- \frac{1}{8} ln ∣ 7 - 8 x ∣ + C

Solution steps

\int \frac{1}{7 - 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 = 7 - 8 x

= - \frac{1}{8} ln ∣ 7 - 8 x ∣

Add a constant to the solution

= - \frac{1}{8} ln ∣ 7 - 8 x ∣ + C

n = 1 \sum \infty 99

k = 1 \sum \infty (- \frac{3}{4})^{k - 1}

\frac{d}{d x} (\frac{1}{x} - x)

\int cos^{8} (4 - x) sin (4 - x) d x

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

What is the integral of 1/((7-8x)) ?
The integral of 1/((7-8x)) is -1/8 ln|7-8x|+C