What is the integral of (15)/(400+5t) ?

The integral of (15)/(400+5t) is 3ln|400+5t|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (15)/(400+5t)

\int \frac{15}{400 + 5 t} d t

3 ln ∣ 400 + 5 t ∣ + C

Solution steps

\int \frac{15}{400 + 5 t} d t

Take the constant out:

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

= 15 \cdot \int \frac{1}{400 + 5 t} d t

Apply u-substitution

: \int \frac{1}{5 u} d u

= 15 \cdot \int \frac{1}{5 u} d u

Take the constant out:

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

= 15 \cdot \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 15 \cdot \frac{1}{5} ln ∣ u ∣

Substitute back

u = 400 + 5 t

= 15 \cdot \frac{1}{5} ln ∣ 400 + 5 t ∣

Simplify

15 \cdot \frac{1}{5} ln ∣ 400 + 5 t ∣ : 3 ln ∣ 400 + 5 t ∣

= 3 ln ∣ 400 + 5 t ∣

Add a constant to the solution

= 3 ln ∣ 400 + 5 t ∣ + C

\int \frac{sec ^{2} ( 2 x )}{tan ( 2 x )} d x

\int \frac{b}{a} \frac{1}{x ^{2} + a ^{2}} d x

\int sin (\frac{x}{x}) d x

\int (3 x - 7)^{2} d x

\int \frac{3 x + 18}{x ^{2} + 8 x + 12} d x

What is the integral of (15)/(400+5t) ?
The integral of (15)/(400+5t) is 3ln|400+5t|+C