< Mentor Note -- thread moved from General Math to the Homework Help forums >Hi all, Calc II finals is 4-5 weeks away...We're on Taylor Series right now, but I wanted to get started early on studying for the final. I have a few questions that are confusing me that I took from a final exam I saw online (not my college): http://www.dawsoncollege.qc.ca/publ...ciplines/math/exams/201-203-dw-winter2012.pdf Problem 1: Find f(x) given f prime (x) = ( 2x^(2/3) - 3x ) / x , and f(8) = 4. I got 3x^(2/3) - 3x I think the integral is correct, but am not sure what to do with the f(8) = 4. What does it mean in relation to this problem? Problem 2: Integral of (2x+3) * (sin(x/2)) -Here, I used Int. by parts --> u = 2x+3, du = 2dx, dV = sin(x/2), V = -2cos(x/2) I ended up with -4xcos(x/2) - 6cos(x/2) + 8sin(x/2) + C <--This is incorrect/partially correct, as per the answers (on the bottom of that page [I can also post them here]). Problem 2B: The Integral of (15+4x-x^2) / (x-1)(x^2 + 5) <---This seems/seemed like a partial fractions problem. I have: A(x^2 + 5) + B(x-1) = 15+4x - x^2 Let x = 1, 6A = 18 --> A = 3. I am stuck here. I can't make x into anything to get rid of the 5. What am I missing here? System of Equations? Completing the square? Would appreciate the guidance. These are what I'm working on. This class has been hard for me, so I'm just trying to work hard and chug through problems. Thanks.