What is the integral of (1-x)^{1/2} ?

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

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integral of (1-x)^{1/2}

integral

(1 - x)^{\frac{1}{2}}

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

Solution steps

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

Apply u-substitution

: \int - u^{\frac{1}{2}} d u

= \int - u^{\frac{1}{2}} d u

Take the constant out:

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

= - \int u^{\frac{1}{2}} d u

Apply the Power Rule

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

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

Substitute back

u = 1 - x

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

Add a constant to the solution

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

x^{2} cos^{2} (x)

sin (t^{2})

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

\frac{x}{1 + cos ( x )}

1 + cos^{2} (x)

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