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

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

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integral of 1/((a-x))

integral

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

- ln ∣ a - x ∣ + C

Solution steps

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = a - x

= - ln ∣ a - x ∣

Add a constant to the solution

= - ln ∣ a - x ∣ + C

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}

in t e g r a l \frac{x}{( x ^{2} + y ^{2} )}

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