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

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 ∣

Add a constant to the solution

= - ln ∣ 2 - x ∣ + C

y^{2} = \frac{1}{8} x, y = 8 x^{2}

f (x) = - x^{3} - 5 x^{2} + 2, at x = - 1

e^{r x}

\frac{d}{d x} ((x^{2} - 3 x)^{2})

\int_{1}^{\infty} \frac{4}{1 + x ^{2}} d x