Show that with limits 3 - 8, ∫(x+1)^1/2 / (x+5) dx = pi + 2 - 4 arctan 3/2.
How can I do this?
Let . Then .
To make it easier, I'll make one more substitution:
and it becomes,
Now use integration by parts to get the answer.
,
There surely must be a shorter way. This is only a brute force attempt to get the integral. I'll think on it again as soon as I have some time (if someone doesn't help you in that time ;p)