What is the integral of 1/(-7x+2) ?

The integral of 1/(-7x+2) is -1/7 ln|-7x+2|+C

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integral of 1/(-7x+2)

\int \frac{1}{- 7 x + 2} d x

- \frac{1}{7} ln ∣ - 7 x + 2 ∣ + C

Solution steps

\int \frac{1}{- 7 x + 2} 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 = - 7 x + 2

= - \frac{1}{7} ln ∣ - 7 x + 2 ∣

Add a constant to the solution

= - \frac{1}{7} ln ∣ - 7 x + 2 ∣ + C

What is the integral of 1/(-7x+2) ?
The integral of 1/(-7x+2) is -1/7 ln|-7x+2|+C