What is the integral of 1/(1.5-0.8x) ?

The integral of 1/(1.5-0.8x) is -1.25ln|1.5-0.8x|+C

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integral of 1/(1.5-0.8x)

\int \frac{1}{1.5 - 0.8 x} d x

- 1.25 ln ∣ 1.5 - 0.8 x ∣ + C

Solution steps

\int \frac{1}{1.5 - 0.8 x} d x

Apply u-substitution

: \int - \frac{1}{0.8 u} d u

= \int - \frac{1}{0.8 u} d u

Take the constant out:

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

= - \frac{1}{0.8} \cdot \int \frac{1}{u} d u

Simplify

= - 1.25 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 1.25 ln ∣ u ∣

Substitute back

u = 1.5 - 0.8 x

= - 1.25 ln ∣ 1.5 - 0.8 x ∣

Add a constant to the solution

= - 1.25 ln ∣ 1.5 - 0.8 x ∣ + C

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What is the integral of 1/(1.5-0.8x) ?
The integral of 1/(1.5-0.8x) is -1.25ln|1.5-0.8x|+C