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

1 Answer
Noah G
May 9, 2018

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

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