What is the integral of (20)/(0.05t+8) ?

The integral of (20)/(0.05t+8) is 400ln|0.05t+8|+C

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integral of (20)/(0.05t+8)

\int \frac{20}{0.05 t + 8} d t

400 ln ∣ 0.05 t + 8 ∣ + C

Solution steps

\int \frac{20}{0.05 t + 8} d t

Take the constant out:

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

= 20 \cdot \int \frac{1}{0.05 t + 8} d t

Apply u-substitution

: \int \frac{1}{0.05 u} d u

= 20 \cdot \int \frac{1}{0.05 u} d u

Take the constant out:

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

= 20 \cdot \frac{1}{0.05} \cdot \int \frac{1}{u} d u

Simplify

= 20 \cdot 20 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 20 \cdot 20 ln ∣ u ∣

Substitute back

u = 0.05 t + 8

= 20 \cdot 20 ln ∣ 0.05 t + 8 ∣

Simplify

= 400 ln ∣ 0.05 t + 8 ∣

Add a constant to the solution

= 400 ln ∣ 0.05 t + 8 ∣ + C

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What is the integral of (20)/(0.05t+8) ?
The integral of (20)/(0.05t+8) is 400ln|0.05t+8|+C