What is the integral of 1/(5x-6) ?

The integral of 1/(5x-6) is 1/5 ln|5x-6|+C

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integral of 1/(5x-6)

\int \frac{1}{5 x - 6} d x

\frac{1}{5} ln ∣ 5 x - 6 ∣ + C

Solution steps

\int \frac{1}{5 x - 6} d x

Apply u-substitution

: \int \frac{1}{5 u} d u

= \int \frac{1}{5 u} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} ln ∣ u ∣

Substitute back

u = 5 x - 6

= \frac{1}{5} ln ∣ 5 x - 6 ∣

Add a constant to the solution

= \frac{1}{5} ln ∣ 5 x - 6 ∣ + C

x \to 0 lim (x cot (2 x))

\int_{0}^{25} \frac{4}{5} x d x

y^{^{'}} + y = 5 \cdot x + 1

\frac{\partial}{\partial z} (x y^{2} z)

y^{^{''}} + 8 y^{^{'}} + 4 y = 0