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

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

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integral of sqrt(3-x)

\int 3 - x d x

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

Solution steps

\int 3 - x d x

Apply u-substitution

: \int - u d u

= \int - u d u

Take the constant out:

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

= - \int u d u

Apply the Power Rule

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

= - \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 3 - x

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

Add a constant to the solution

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

\frac{3}{( x - 7 ) ^{4}}

\frac{d}{d x} (\frac{x ^{4}}{8} + \frac{x ^{2}}{6} - \frac{x}{5} + \frac{1}{7})

\int e^{c s c (2 x)} csc (2 x) cot (2 x) d x

16 y^{^{''}} - 8 y^{^{'}} + y = 0

4 e^{- t} + 2

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