What is the integral of 1/(5-t) ?

The integral of 1/(5-t) is -ln|5-t|+C

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integral of 1/(5-t)

\int \frac{1}{5 - t} d t

- ln ∣ 5 - t ∣ + C

Solution steps

\int \frac{1}{5 - t} d t

Apply u-substitution

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

= \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 = 5 - t

= - ln ∣ 5 - t ∣

Add a constant to the solution

= - ln ∣ 5 - t ∣ + C

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