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

The integral of (y+1)sqrt(1-y) is -2/3 (y+1)(1-y)^{3/2}-4/15 (1-y)^{5/2}+C

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integral of (y+1)sqrt(1-y)

\int (y + 1) 1 - y d y

- \frac{2}{3} (y + 1) (1 - y)^{\frac{3}{2}} - \frac{4}{15} (1 - y)^{\frac{5}{2}} + C

Solution steps

\int (y + 1) 1 - y d y

Apply Integration By Parts

: - \frac{2}{3} (y + 1) (1 - y)^{\frac{3}{2}} - \int - \frac{2}{3} (1 - y)^{\frac{3}{2}} d y

= - \frac{2}{3} (y + 1) (1 - y)^{\frac{3}{2}} - \int - \frac{2}{3} (1 - y)^{\frac{3}{2}} d y

\int - \frac{2}{3} (1 - y)^{\frac{3}{2}} d y = \frac{4}{15} (1 - y)^{\frac{5}{2}}

= - \frac{2}{3} (y + 1) (1 - y)^{\frac{3}{2}} - \frac{4}{15} (1 - y)^{\frac{5}{2}}

Add a constant to the solution

= - \frac{2}{3} (y + 1) (1 - y)^{\frac{3}{2}} - \frac{4}{15} (1 - y)^{\frac{5}{2}} + C

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What is the integral of (y+1)sqrt(1-y) ?
The integral of (y+1)sqrt(1-y) is -2/3 (y+1)(1-y)^{3/2}-4/15 (1-y)^{5/2}+C