5x
(x-1)((x^2)+4)
fractions?
5x = A + B
(x-1) ?
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.
You can use partial fractions with this setup
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.
Good luck.
Here's another way using trig.
Let
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.