What is the integral of sqrt(5-y) ?

The integral of sqrt(5-y) is -2/3 (5-y)^{3/2}+C

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integral of sqrt(5-y)

\int 5 - y d y

- \frac{2}{3} (5 - y)^{\frac{3}{2}} + C

Solution steps

\int 5 - y d y

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 = 5 - y

= - \frac{2}{3} (5 - y)^{\frac{3}{2}}

Add a constant to the solution

= - \frac{2}{3} (5 - y)^{\frac{3}{2}} + C

\frac{1}{2 r} + \frac{1}{4 r ^{\frac{3}{4}}}

x

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

arctan (\frac{x}{2})

x \to \infty lim ((ln (x))^{\frac{1}{x ^{2}}})

What is the integral of sqrt(5-y) ?
The integral of sqrt(5-y) is -2/3 (5-y)^{3/2}+C