What is the integral of 1/((2-3x)) ?

The integral of 1/((2-3x)) is -1/3 ln|2-3x|+C

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integral of 1/((2-3x))

\int \frac{1}{( 2 - 3 x )} d x

- \frac{1}{3} ln ∣ 2 - 3 x ∣ + C

Solution steps

\int \frac{1}{2 - 3 x} d x

Apply u-substitution

: \int - \frac{1}{3 u} d u

= \int - \frac{1}{3 u} d u

Take the constant out:

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

= - \frac{1}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{3} ln ∣ u ∣

Substitute back

u = 2 - 3 x

= - \frac{1}{3} ln ∣ 2 - 3 x ∣

Add a constant to the solution

= - \frac{1}{3} ln ∣ 2 - 3 x ∣ + C

\int \frac{7}{x ^{2}} d x

\int 20 x^{3} d x

\frac{d Q}{d t} = 0.03 (1 - Q)^{\frac{2}{3}}

n = 1 \sum \infty \frac{e ^{nπ}}{π ^{n e}}

y^{^{''}} - 3 y^{^{'}} - 54 y = 0

What is the integral of 1/((2-3x)) ?
The integral of 1/((2-3x)) is -1/3 ln|2-3x|+C