1. The problem statement, all variables and given/known data I've run into this problem a few times, where I get the right answer, but multiplied by a constant where I would have it divided by the constant or vice versa. "First make a substitution and then use integration by parts to evaluate the integral" ∫cos(√x)dx 2. Relevant equations ∫udv = uv - ∫vdu 3. The attempt at a solution let A = √x dA = dx/(2√x) 2(√x)dA = dx A2 = x 2∫Acos(A)dA let u=A du=dA dv= cos(A) v = sin A + C 2∫Acos(A)dA = Asin(A) - ∫sin(A) = Asin(A) + cos(A) so, then ∫Acos(A)dA = (Asin(A) +cos(A))/2 +C this is wrong, it should be 2Asin(A) + 2cos(A) + C and im not sure where exactly I can remedy this. I think my problem might be with 2∫Acos(A)dA = Asin(A) - ∫sin(A) since I have an integral im evaluating by parts multiplied by a constant, does 2∫Acos(A)dA = Asin(A) - ∫sin(A) => 2∫Acos(A)dA = 2(Asin(A) - ∫sin(A)) ??? or more generally c∫udv = c(uv - ∫vdu) ?