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

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

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integral of 1/((x-2))

integral

\frac{1}{( x - 2 )}

ln ∣ x - 2 ∣ + C

Solution steps

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x - 2

= ln ∣ x - 2 ∣

Add a constant to the solution

= ln ∣ x - 2 ∣ + C

in t e g r a l \frac{t ^{2}}{( 1 - t ^{2} )}

in t e g r a l \frac{1}{( a - x )}

in t e g r a l \frac{8}{( x ^{3} - 16 x )}

in t e g r a l \frac{x}{( x + 1 )}

in t e g r a l 3 x^{3}