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

36 y^{^{''}} - y = x e^{\frac{x}{6}}

3 x + 8

\int \frac{3 x + 6}{( 2 x ^{2} + 8 x + 3 ) ^{2}} d x

y = \frac{8}{x - 2}, at x = 6

\frac{d}{d x} (26 e^{x^{2}} x)