What is the integral of sqrt(1-x) ?

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

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integral of sqrt(1-x)

integral

1 - x

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

Solution steps

\int 1 - 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 = 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

lo g_{10} (1 + x^{2})

x^{2} - x + 1

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

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

\frac{x + 1}{x ^{2} + x + 6}

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