Hi everybody I'm having a lot of trouble remembering all of the formulas for differentiating inverse trig functions, for integrating trig functions, or integrating inverse trig functions, or integrating hyperbolic trig functions, or integrating inverse hyperbolic trig functions. Luckily, in differentiating inverse trig functions I can invert the equation & use implicit differentiation & rederive all 6 trig functions all just by knowing how to differentiate trig functions. That to me is a lot smarter & better than cheating by memorizing formulas as there is simple logic involved. However, I've had so much trouble trying to deal with the rest of these functions in a logical way & every source I check tells me to just use the formula's I've memorized. Thomas Calculus Stewart Calculus Apostol Calculus Calculus Made Easy The Calculus Lifesaver Loads of youtube videos Loads of internet pdf's and sites I've had some success with a particular triangle method, i.e. look for the sum of two perfect squares in a denominator under a square root in the denominator, that means you can draw a triangle & use a very similar logic to rederive your way to the answer according to the situation. Namely the logic purported in this and this. However, what about all these seperate cases, inverse trig functions, hyperbolic trig inverse hyperbolic trig Have all of you just memorized the formula's to just plug in every time you recognise the shape of the equation? If not I'd be so happy to hear of sources to where you learned this smart way that I seem to be missing. I've had so much trouble with calculus in that I have to ignore my books & search out the real secret behind each method in calculus, for instance; Newtons method is just an algebraic manipulation of the point-slope form of an equation, two seconds to rederive it. Linear Approximation is another manipulation of this simple equation in a slightly different way. Mean Value Theorem is just Rolle's Theorem slanted. Integral MVT is just standard averaging calc'd up. All of that shells and washers stuff is just geometry & a flavour of calc. There just has to be some way to look at trig integrals in a similarly logical way.