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

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

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integral of-1/(2-x)

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

ln ∣ 2 - x ∣ + C

Solution steps

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

Take the constant out:

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

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

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 = 2 - x

= - (- ln ∣ 2 - x ∣)

Simplify

= ln ∣ 2 - x ∣

Add a constant to the solution

= ln ∣ 2 - x ∣ + C

f (x) = cot^{5} (x)

(x^{2} - y^{2}) d x + x y d y = 0

\int_{7}^{13} \frac{y}{y ^{2} - 3 y - 4} d y

f^{^{'''}} (x) = 6 (x^{- 2})

\frac{s + 10}{s ^{2} - s - 2}