What is the integral of 3/(50+2t) ?

The integral of 3/(50+2t) is 3/2 ln|50+2t|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3/(50+2t)

\int \frac{3}{50 + 2 t} d t

\frac{3}{2} ln ∣ 50 + 2 t ∣ + C

Solution steps

\int \frac{3}{50 + 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}{50 + 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 = 50 + 2 t

= 3 \cdot \frac{1}{2} ln ∣ 50 + 2 t ∣

Simplify

3 \cdot \frac{1}{2} ln ∣ 50 + 2 t ∣ : \frac{3}{2} ln ∣ 50 + 2 t ∣

= \frac{3}{2} ln ∣ 50 + 2 t ∣

Add a constant to the solution

= \frac{3}{2} ln ∣ 50 + 2 t ∣ + C

\frac{d}{d x} (- 2 cos (x) + 3 x^{3})

\frac{d}{d x} (x^{2} + 5 x)

\int_{0}^{π} sin (\frac{x}{2}) d x

\int \frac{1 + x ^{2} + 1}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

\int 17 x e^{- x^{2}} d x

What is the integral of 3/(50+2t) ?
The integral of 3/(50+2t) is 3/2 ln|50+2t|+C