What is the integral of (21)/(0.07t+5) ?

The integral of (21)/(0.07t+5) is 300ln|0.07t+5|+C

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integral of (21)/(0.07t+5)

\int \frac{21}{0.07 t + 5} d t

300 ln ∣ 0.07 t + 5 ∣ + C

Solution steps

\int \frac{21}{0.07 t + 5} d t

Take the constant out:

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

= 21 \cdot \int \frac{1}{0.07 t + 5} d t

Apply u-substitution

: \int \frac{1}{0.07 u} d u

= 21 \cdot \int \frac{1}{0.07 u} d u

Take the constant out:

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

= 21 \cdot \frac{1}{0.07} \cdot \int \frac{1}{u} d u

Simplify

= 21 \cdot 14.28571 \dots \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 21 \cdot 14.28571 \dots ln ∣ u ∣

Substitute back

u = 0.07 t + 5

= 21 \cdot 14.28571 \dots ln ∣ 0.07 t + 5 ∣

Simplify

= 300 ln ∣ 0.07 t + 5 ∣

Add a constant to the solution

= 300 ln ∣ 0.07 t + 5 ∣ + C

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What is the integral of (21)/(0.07t+5) ?
The integral of (21)/(0.07t+5) is 300ln|0.07t+5|+C