What is the integral of 2/(3x+5) ?

The integral of 2/(3x+5) is 2/3 ln|3x+5|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2/(3x+5)

\int \frac{2}{3 x + 5} d x

\frac{2}{3} ln ∣ 3 x + 5 ∣ + C

Solution steps

\int \frac{2}{3 x + 5} d x

Take the constant out:

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

= 2 \cdot \int \frac{1}{3 x + 5} d x

Apply u-substitution

: \int \frac{1}{3 u} d u

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 \cdot \frac{1}{3} ln ∣ u ∣

Substitute back

u = 3 x + 5

= 2 \cdot \frac{1}{3} ln ∣ 3 x + 5 ∣

Simplify

2 \cdot \frac{1}{3} ln ∣ 3 x + 5 ∣ : \frac{2}{3} ln ∣ 3 x + 5 ∣

= \frac{2}{3} ln ∣ 3 x + 5 ∣

Add a constant to the solution

= \frac{2}{3} ln ∣ 3 x + 5 ∣ + C

\int_{1}^{8} t ln (t) d t

\int_{0}^{4} x (0.5 - 0.125 x) d x

y^{^{''}} = 2

\frac{\partial}{\partial x} (K (x)^{\frac{1}{3}} L^{\frac{2}{3}})

\frac{d}{d x} (5 x^{- 5} - 6 x^{- 2} + 13 x^{- 1})