The second integral is already a partial fraction, apply integration by parts.
I am doing this problem:
integral of (x^3 + x - 1)/((X^2 +1))^2 dx
So i set that integral equal to (Ax + B)/(x^2 + 1) + (Cx + D)/((x^2 + 1))^2
I got ax^3 + ax + bx^2 + b + cx + d = 1x^3 + 1x - 1
x^3 terms: a = 1
x^2 terms: b = 0
x^1 terms: a + c = 1 ( c = 0)
x^0 terms: b + d = -1 ( d = -1)
I put these back into the equation and got
integral of 1/(x^2 + 1) + integral of -1/((x^2 + 1))^2
which equals ln(x^2 + 1) + 1/(x^2 + 1) + C
The answer in the book has those 2 first terms as the answer..but has 2 more terms, then the Constant..I am having trouble finding the correct answer. What did I do wrong?