What is the integral of 3/(x-1) ?

The integral of 3/(x-1) is 3ln|x-1|+C

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integral of 3/(x-1)

\int \frac{3}{x - 1} d x

3 ln ∣ x - 1 ∣ + C

Solution steps

\int \frac{3}{x - 1} 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}{x - 1} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 ln ∣ u ∣

Substitute back

u = x - 1

= 3 ln ∣ x - 1 ∣

Add a constant to the solution

= 3 ln ∣ x - 1 ∣ + C

3 x^{5} - 20 x^{3}

8 x, \frac{1}{2} x, 1, 2

\int (y^{2}) d y

\frac{d y}{d x} + y^{2} = 1

\frac{d}{d x} (y^{2} - x^{2} + 2)