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

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

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integral of 1/(1-7x)

\int \frac{1}{1 - 7 x} d x

- \frac{1}{7} ln ∣ 1 - 7 x ∣ + C

Solution steps

\int \frac{1}{1 - 7 x} d x

Apply u-substitution

= \int - \frac{1}{7 u} d u

Take the constant out:

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

= - \frac{1}{7} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{7} ln ∣ u ∣

Substitute back

u = 1 - 7 x

= - \frac{1}{7} ln ∣ 1 - 7 x ∣

Add a constant to the solution

= - \frac{1}{7} ln ∣ 1 - 7 x ∣ + C