What is the integral of sqrt(2x+9) ?

The integral of sqrt(2x+9) is 1/3 (2x+9)^{3/2}+C

Popular >

integral of sqrt(2x+9)

\int 2 x + 9 d x

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

Solution steps

\int 2 x + 9 d x

Apply u-substitution

: \int \frac{u}{2} d u

= \int \frac{u}{2} d u

Take the constant out:

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

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

Apply the Power Rule

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

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

Substitute back

u = 2 x + 9

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

Simplify

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

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

Add a constant to the solution

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

2 t y^{^{'}} - 3 y = 0

f (x) = \frac{7}{x ^{4}}, at x = - 3

y = x + 2, (- 1, 1)

\frac{d y}{d x} = \frac{y ^{2} + x y + x ^{2}}{x ^{2}}, y (1) = - 1

x \to - 4 + lim (\frac{- 2}{x ^{2} - 16})

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