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

The integral of sqrt(3x+5) is 2/9 (3x+5)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sqrt(3x+5)

\int 3 x + 5 d x

\frac{2}{9} (3 x + 5)^{\frac{3}{2}} + C

Solution steps

\int 3 x + 5 d x

Apply u-substitution

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

= \int \frac{u}{3} d u

Take the constant out:

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

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

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

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

Substitute back

u = 3 x + 5

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

Simplify

\frac{1}{3} \cdot \frac{2}{3} (3 x + 5)^{\frac{3}{2}} : \frac{2}{9} (3 x + 5)^{\frac{3}{2}}

= \frac{2}{9} (3 x + 5)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{9} (3 x + 5)^{\frac{3}{2}} + C

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

\int \frac{13 x ^{3}}{3 + x ^{2}} d x

\int sin^{5} (x co) s^{2} x d x

\int \frac{4}{6 - 2 x} d x

What is the integral of sqrt(3x+5) ?
The integral of sqrt(3x+5) is 2/9 (3x+5)^{3/2}+C