What is the integral of 3/(-5x+2) ?

The integral of 3/(-5x+2) is -3/5 ln|-5x+2|+C

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integral of 3/(-5x+2)

\int \frac{3}{- 5 x + 2} d x

- \frac{3}{5} ln ∣ - 5 x + 2 ∣ + C

Solution steps

\int \frac{3}{- 5 x + 2} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{- 5 x + 2} d x

Apply u-substitution

: \int - \frac{1}{5 u} d u

= 3 \cdot \int - \frac{1}{5 u} d u

Take the constant out:

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

= 3 (- \frac{1}{5} \cdot \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 (- \frac{1}{5} ln ∣ u ∣)

Substitute back

u = - 5 x + 2

= 3 (- \frac{1}{5} ln ∣ - 5 x + 2 ∣)

Simplify

3 (- \frac{1}{5} ln ∣ - 5 x + 2 ∣) : - \frac{3}{5} ln ∣ - 5 x + 2 ∣

= - \frac{3}{5} ln ∣ - 5 x + 2 ∣

Add a constant to the solution

= - \frac{3}{5} ln ∣ - 5 x + 2 ∣ + C

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What is the integral of 3/(-5x+2) ?
The integral of 3/(-5x+2) is -3/5 ln|-5x+2|+C