What is the integral of 1/(7-3x) ?

The integral of 1/(7-3x) is -1/3 ln|7-3x|+C

Popular >

integral of 1/(7-3x)

\int \frac{1}{7 - 3 x} d x

- \frac{1}{3} ln ∣ 7 - 3 x ∣ + C

Solution steps

\int \frac{1}{7 - 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 = 7 - 3 x

= - \frac{1}{3} ln ∣ 7 - 3 x ∣

Add a constant to the solution

= - \frac{1}{3} ln ∣ 7 - 3 x ∣ + C

y^{^{'}} = 9 x + y

(2 e^{y} - x) (\frac{d y}{d x}) = 1

f (x) = - 7 e^{- 3 x} - 6 e^{- 3 x} x

x \to 3 lim (\frac{x ^{2} - 8}{x - 3})

\frac{d}{d x} (x - 3 x^{2} + 8 x^{- 2})