What is the integral of 4/(sqrt(3x+5)) ?

The integral of 4/(sqrt(3x+5)) is 8/3 sqrt(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 4/(sqrt(3x+5))

\int \frac{4}{3 x + 5} d x

\frac{8}{3} 3 x + 5 + C

Solution steps

\int \frac{4}{3 x + 5} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{3 x + 5} d x

Apply u-substitution

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

= 4 \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

= 4 \cdot \frac{1}{3} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 4 \cdot \frac{1}{3} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 3 x + 5

= 4 \cdot \frac{1}{3} \cdot 2 (3 x + 5)^{\frac{1}{2}}

Simplify

4 \cdot \frac{1}{3} \cdot 2 (3 x + 5)^{\frac{1}{2}} : \frac{8}{3} 3 x + 5

= \frac{8}{3} 3 x + 5

Add a constant to the solution

= \frac{8}{3} 3 x + 5 + C

\int 8 + 8 cos (x) d x

\int \frac{1}{x ^{3} 9 - x ^{2}} d x

\int (4 x^{3} - 5) d x

\int \frac{1}{x ( 1 - 7 x )} d x

\int \frac{3 t ^{2} - 3}{t ^{3} - 3 t} d t

What is the integral of 4/(sqrt(3x+5)) ?
The integral of 4/(sqrt(3x+5)) is 8/3 sqrt(3x+5)+C