u = ln(x) and dv = 1 du = 1/x and v = x integral ln(x) = x ln(x) - integral 1/x times x integral ln(x) = x ln(x) - x + C I could give integral arctan(x) b

u = ln(x) and dv = 1 du = 1/x and v = x integral ln(x) = x ln(x) - integral 1/x times x integral ln(x) = x ln(x) - x + C I could give integral arctan(x) but with the advent of computer algebra systems I'm mostly interested in them knowing the basic examples and to not burden them on a test with something more complicated. EDIT: The derivative of 1/x is not ln(x) as you stated. You got it backwards and my guess is that is the source of your confusion.