What is the integral of sqrt(6x+5) ?

The integral of sqrt(6x+5) is 1/9 (6x+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(6x+5)

\int 6 x + 5 d x

\frac{1}{9} (6 x + 5)^{\frac{3}{2}} + C

Solution steps

\int 6 x + 5 d x

Apply u-substitution

: \int \frac{u}{6} d u

= \int \frac{u}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{6} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 6 x + 5

= \frac{1}{6} \cdot \frac{2}{3} (6 x + 5)^{\frac{3}{2}}

Simplify

\frac{1}{6} \cdot \frac{2}{3} (6 x + 5)^{\frac{3}{2}} : \frac{1}{9} (6 x + 5)^{\frac{3}{2}}

= \frac{1}{9} (6 x + 5)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{9} (6 x + 5)^{\frac{3}{2}} + C

sin (y) = 5 x^{3} - 5

f (x) = x^{2} - x + 1, at x = - 1

h \to 0 lim (6 x + 3 h)

\frac{d}{d x} (1 + 2 x)

\frac{\partial}{\partial x} (x y^{2} + x)

What is the integral of sqrt(6x+5) ?
The integral of sqrt(6x+5) is 1/9 (6x+5)^{3/2}+C