What is the integral of 1/(0.15x+20) ?

The integral of 1/(0.15x+20) is 6.66666…ln|0.15x+20|+C

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integral of 1/(0.15x+20)

\int \frac{1}{0.15 x + 20} d x

6.66666 \dots ln ∣ 0.15 x + 20 ∣ + C

Solution steps

\int \frac{1}{0.15 x + 20} d x

Apply u-substitution

= \int \frac{1}{0.15 u} d u

Take the constant out:

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

= \frac{1}{0.15} \cdot \int \frac{1}{u} d u

Simplify

= 6.66666 \dots \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 6.66666 \dots ln ∣ u ∣

Substitute back

u = 0.15 x + 20

= 6.66666 \dots ln ∣ 0.15 x + 20 ∣

Add a constant to the solution

= 6.66666 \dots ln ∣ 0.15 x + 20 ∣ + C

f (n) = 2^{n}

\int 9 x cos (2 x) d x

a re a y = x^{2} - 1, (- 1, 1)

a re a y = x - 6, y^{2} = x

d er i v a t i v e tan^{2} (5 x)

What is the integral of 1/(0.15x+20) ?
The integral of 1/(0.15x+20) is 6.66666…ln|0.15x+20|+C