Question

Evaluate this integral of ydy/√y+1 using substitution method?

Answer 1

The integral equals `2/3(y + 1)^(3/2) - 2(y + 1)^(1/2) + C`

Explanation:

We have:

`I = int y/sqrt(y + 1) dy`

Now let `u = y + 1`. Then `du = dy`.

`I = int (u - 1)/sqrt(u) du`

`I = int u/sqrt(u) - 1/sqrt(u)du`

`I = int u^(1/2) - u^(-1/2)du`

`I = 2/3u^(3/2) - 2u^(1/2) + C`

`I = 2/3(y + 1)^(3/2) - 2(y + 1)^(1/2) + C`

Hopefully this helsp1