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

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

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integral of sqrt(-x+1)

\int - x + 1 d x

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

Solution steps

\int - x + 1 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 = - x + 1

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

Add a constant to the solution

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

\int \frac{x - 3}{x - 2} d x

\int 2 y e^{y} d y

\int \frac{e ^{- \frac{1}{x}}}{4 x ^{2}} d x

\int x^{4} - \frac{1}{x ^{2}} + 1 d x

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