What is the integral of 1/(5x+16) ?

The integral of 1/(5x+16) is 1/5 ln|5x+16|+C

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integral of 1/(5x+16)

\int \frac{1}{5 x + 16} d x

\frac{1}{5} ln ∣ 5 x + 16 ∣ + C

Solution steps

\int \frac{1}{5 x + 16} 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 + 16

= \frac{1}{5} ln ∣ 5 x + 16 ∣

Add a constant to the solution

= \frac{1}{5} ln ∣ 5 x + 16 ∣ + C

y = 9 x^{2}, y = x^{2} + 7

h \to 0 lim (2 x h)

n = 5 \sum \infty \frac{1}{n ^{2}}

\int (\frac{1}{y} sin (\frac{x}{y}) + x) d x

\frac{d}{d x} (arctan (e^{x} + 1))

What is the integral of 1/(5x+16) ?
The integral of 1/(5x+16) is 1/5 ln|5x+16|+C