5x = A + B
And ((x^2)+4) is 1/2arctan(x/2)
the answer key says
ln|x-1| -.5ln|x^2+4| - 2arctan(x/2)
Can anyone help? Thanks.
Or observe that
Now we have
The first is in the form of the arctangent or if you want to do it by hand let x=2tan(u) the 2nd is a u sub on the denominator and the last one is a u sub on the denominator .
I hope this helps.
Here's another way using trig.
Making the subs we get a menacing looking thing, but it simplifies down fairly nice.
Making the subs we get:
This, believe it or not, whittles down to
Then, after integrating, resub in
You may wish to stick with the others methods. I just threw it out there.