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

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

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integral of (sqrt(3x+2))

\int (3 x + 2) d x

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

Solution steps

\int 3 x + 2 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 + 2

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

Simplify

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

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

Add a constant to the solution

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

y = 19 cos (\frac{x}{b} - 2.5) + 19

\frac{\partial}{\partial x} (sin^{2} (2 x + 3 y))

\int_{0}^{1} x^{2} (x^{3} - 2)^{3} d x

\frac{\partial}{\partial x} (\frac{t}{x})

\frac{d y}{d x} + (\frac{3}{x}) y = - 4 x - 10

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