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

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

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integral of sqrt(2-3x)

\int 2 - 3 x d x

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

Solution steps

\int 2 - 3 x 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 = 2 - 3 x

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

Simplify

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

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (4 y^{8} + 3 y^{2} x^{2})

(x^{2} + y^{2}) d x = 2 x y d y

ln (1 + e^{- x})

\int \frac{1}{x ^{\frac{2}{3}} ( 2 + x ^{\frac{1}{3}} )} d x

\int sin (t) d t

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