What is the integral of 1/((pix-1)) ?

The integral of 1/((pix-1)) is 1/pi ln|pix-1|+C

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integral of 1/((pix-1))

\int \frac{1}{( π x - 1 )} d x

\frac{1}{π} ln ∣ π x - 1 ∣ + C

Solution steps

\int \frac{1}{π x - 1} d x

Apply u-substitution

: \int \frac{1}{π u} d u

= \int \frac{1}{π u} d u

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{π} ln ∣ u ∣

Substitute back

u = π x - 1

= \frac{1}{π} ln ∣ π x - 1 ∣

Add a constant to the solution

= \frac{1}{π} ln ∣ π x - 1 ∣ + C

\int 4^{l n (x)} d x

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = 0

(1, 7), (10, 1)

\int sin (x) x d x

2 sin (x) + 2 x cos (x)

What is the integral of 1/((pix-1)) ?
The integral of 1/((pix-1)) is 1/pi ln|pix-1|+C