What is the integral of 2/(200+t) ?

The integral of 2/(200+t) is 2ln|200+t|+C

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integral of 2/(200+t)

\int \frac{2}{200 + t} d t

2 ln ∣ 200 + t ∣ + C

Solution steps

\int \frac{2}{200 + t} d t

Take the constant out:

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

= 2 \cdot \int \frac{1}{200 + t} d t

Apply u-substitution

= 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 ln ∣ u ∣

Substitute back

u = 200 + t

= 2 ln ∣ 200 + t ∣

Add a constant to the solution

= 2 ln ∣ 200 + t ∣ + C