What is the integral of 1/(0.2x+3) ?

The integral of 1/(0.2x+3) is 5ln|0.2x+3|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(0.2x+3)

\int \frac{1}{0.2 x + 3} d x

5 ln ∣ 0.2 x + 3 ∣ + C

Solution steps

\int \frac{1}{0.2 x + 3} d x

Apply u-substitution

: \int \frac{1}{0.2 u} d u

= \int \frac{1}{0.2 u} d u

Take the constant out:

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

= \frac{1}{0.2} \cdot \int \frac{1}{u} d u

Simplify

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 ln ∣ u ∣

Substitute back

u = 0.2 x + 3

= 5 ln ∣ 0.2 x + 3 ∣

Add a constant to the solution

= 5 ln ∣ 0.2 x + 3 ∣ + C

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

\int (x^{2} \cdot cos (x)) d x

\int e^{9 x} + 5 e^{- x} d x

\int \frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} + 6 x + C d x

\int e^{5 - 4 x} d x

What is the integral of 1/(0.2x+3) ?
The integral of 1/(0.2x+3) is 5ln|0.2x+3|+C