After you complete the square
let
so your integral looks like this
From here use half angle formula
and you get
Now that should be an easier integral to evaluate and back substitute for u
&
What should I do at this point? I considered expanding the square, but that seems to make things more messy and it seems like something else should be going on. It also didn't seem to lead me to an answer either. Thanks!
I was wondering why your answer differed slightly from my books answer and I found the problem here...
However, I believe that if then .
This will make the final answer:
I also don't understand how you did this step, could you go into more detail please?:
Now so you can see this more clearly lets make some substitiutions for the second intergal
Now back substitute for u
so this is what you should get
now you have to back substitute for the other substituion used
Also using the identity
Ok to find out what is you have to remember that we substituted
so to find you use arctan
now to find out what are you need to know
You can figure these out because you are given
so all you have to do is find out what the hypotenuse is since you are already given the opposite and adjacent
So after alot of typing lol your final integral should look like this
Right, 11rdc11. I was getting fouled up because Shyam had not integrated correctly and it took me a bit to catch this.
Also, the values he put for and should have included sqrt in the denominator.
In the end, I can only say that it helped me hone some of my math skills
But, thanks to both of you for the help! I finally figured it out!
Final answer: