What is the integral of 1/(0.37x-0.03) ?

The integral of 1/(0.37x-0.03) is 2.70270…ln|0.37x-0.03|+C

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integral of 1/(0.37x-0.03)

\int \frac{1}{0.37 x - 0.03} d x

2.70270 \dots ln ∣ 0.37 x - 0.03 ∣ + C

Solution steps

\int \frac{1}{0.37 x - 0.03} d x

Apply u-substitution

: \int \frac{1}{0.37 u} d u

= \int \frac{1}{0.37 u} d u

Take the constant out:

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

= \frac{1}{0.37} \cdot \int \frac{1}{u} d u

Simplify

= 2.70270 \dots \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2.70270 \dots ln ∣ u ∣

Substitute back

u = 0.37 x - 0.03

= 2.70270 \dots ln ∣ 0.37 x - 0.03 ∣

Add a constant to the solution

= 2.70270 \dots ln ∣ 0.37 x - 0.03 ∣ + C

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What is the integral of 1/(0.37x-0.03) ?
The integral of 1/(0.37x-0.03) is 2.70270…ln|0.37x-0.03|+C