How do I solve this Integral? (Pic attached in link)

Question

I have been stuck on this integral for 3 hours. Here is what I have so far.. : https://ibb.co/mWAC7x

Answer 1

 

 THe answer is arctan(x+1) + ln|x-1|+c

 

the partial fraction decomposition is 1/(x^2+2x+2)^2 + 1/(x-1)

Answer 2

You just have to do the Partial Fractions part of the job correctly.

What I recommend is finding a common denominator for the right hand side.Then simplify the numerator portion of the right side; having done that, DISCARD THE COMMON DENOMINATORS, and collect LIKE terms on the right side, obtaining a coefficient for each of the different power of x.

 

Then, for each side of the equation, you equate coefficients of the various powers of x.

You then have a system of linear equations involving A through E. To solve that system, my favorite method is to use the RREF function within the MATRIX options of a TI-84 (or -83) calculator.