1. The problem statement, all variables and given/known data A tank initially contains 180 gallons of water in which 8grams of salt are dissolved. Water containing 9 grams of salt per gallon enters the tank at the rate of 3 gallons per minute, and the well mixed solution leaves the tank at the rate of 1 gallon per minute. The equation for the amount of salt in the tank for anytime t. 2. Relevant equations 3. The attempt at a solution My confusion is with the integrating factor. First off I know: Q' = rate at which salt enters - rate at which salt leaves Q' = (9 grams/gal)(3 gal/min) - Q/(180 + 2t) Simplify to Differential equation format Q' + Q/(180 + 2t) = 27 Find the integrating factor. u = e∫1/(180 + 2t) dt = e1/2 ln(180 + 2t) My question is how do you know to move the 1/2 into the power to give the integrating factor u as: u = (180 + 2t)1/2 I know it's a logarithmic law that I can move the coefficient into the power, but how do I recognize that I need to do this here? What's wrong with leaving the half in front as: u = 1/2(180 + 2t) Guidance would be appreciated. Thank you.