What is the integral of 3/(100+2t) ?

The integral of 3/(100+2t) is 3/2 ln|100+2t|+C

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integral of 3/(100+2t)

\int \frac{3}{100 + 2 t} d t

\frac{3}{2} ln ∣ 100 + 2 t ∣ + C

Solution steps

\int \frac{3}{100 + 2 t} d t

Take the constant out:

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

= 3 \cdot \int \frac{1}{100 + 2 t} d t

Apply u-substitution

: \int \frac{1}{2 u} d u

= 3 \cdot \int \frac{1}{2 u} d u

Take the constant out:

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

= 3 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 \cdot \frac{1}{2} ln ∣ u ∣

Substitute back

u = 100 + 2 t

= 3 \cdot \frac{1}{2} ln ∣ 100 + 2 t ∣

Simplify

3 \cdot \frac{1}{2} ln ∣ 100 + 2 t ∣ : \frac{3}{2} ln ∣ 100 + 2 t ∣

= \frac{3}{2} ln ∣ 100 + 2 t ∣

Add a constant to the solution

= \frac{3}{2} ln ∣ 100 + 2 t ∣ + C

\int_{0}^{1} 18 \frac{1}{x ^{p}} d x

y = x (1 - 2 x)^{3}, (1, - 1)

\frac{\partial}{\partial y} (x^{3} ln (y^{6}))

n \to \infty lim (n^{2} + 2)

What is the integral of 3/(100+2t) ?
The integral of 3/(100+2t) is 3/2 ln|100+2t|+C