What is the integral of y((y+7)^{(1/2)}) ?

The integral of y((y+7)^{(1/2)}) is 2/3 y(y+7)^{3/2}-4/15 (y+7)^{5/2}+C

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integral of y((y+7)^{(1/2)})

\int y ((y + 7)^{(\frac{1}{2})}) d y

\frac{2}{3} y (y + 7)^{\frac{3}{2}} - \frac{4}{15} (y + 7)^{\frac{5}{2}} + C

Solution steps

\int y (y + 7)^{\frac{1}{2}} d y

Apply Integration By Parts

= \frac{2}{3} y (y + 7)^{\frac{3}{2}} - \int \frac{2}{3} (y + 7)^{\frac{3}{2}} d y

\int \frac{2}{3} (y + 7)^{\frac{3}{2}} d y = \frac{4}{15} (y + 7)^{\frac{5}{2}}

= \frac{2}{3} y (y + 7)^{\frac{3}{2}} - \frac{4}{15} (y + 7)^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{3} y (y + 7)^{\frac{3}{2}} - \frac{4}{15} (y + 7)^{\frac{5}{2}} + C

What is the integral of y((y+7)^{(1/2)}) ?
The integral of y((y+7)^{(1/2)}) is 2/3 y(y+7)^{3/2}-4/15 (y+7)^{5/2}+C