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

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

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integral of 1/((x-a))

integral

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

ln ∣ x - a ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x - a

= ln ∣ x - a ∣

Add a constant to the solution

= ln ∣ x - a ∣ + C

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

\frac{8 x}{( x ^{4} + 1 )}

\frac{1}{( 1 + x ^{2} ) ^{3}}

csc^{4} (x)

\frac{x ^{3}}{( x ^{2} + 1 )}