1. The problem statement, all variables and given/known data So, I have a trigonometric substitution integration problem. The working is rather hairy, but I've gotten to the point where you draw the triangle to express theta in terms of x. But that's where I'm stuck! I think I may be having trouble with the constant of integration, but I'm not sure! 2. Relevant equations So...for the sides of the triangle I have: Opposite: √[(x+½)2 - ¾] Hypotenuse: x+½ Adjacent: √(¾) My equation is tanθ-[½(ln|secθ+tanθ|)] and I want to express it in terms of x. 3. The attempt at a solution So I just plug it in, Opposite/Adjacent and Hypotenuse/Adjacent but I'm getting it wrong. I get √[(x+½)2 - ¾] / √¾ - ½ln|x + ½ + √[(x+½)2-¾]| / √(¾) Which equals √(x2+x+1)/√¾ - ½ln|x+½+√(x2+x+1) + C But it doesn't, the answer given is √(x2+x+1) - ½ln|x+½+√(x2+x+1), as in the only difference is the denominator for the first term. But I don't understand how it could be integrated into the integration constant, it's not a constant, it's dividing the variable x, no? Or is something else entirely wrong with it!?Any help would be greatly appreciated!