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We had yesterday class where we discussed about this problem and this was a solution. The teacher called it "trick" mathematics. He said you just have to invent what formula do you use. The second option could be using trigonometrical functions or something like that in change of variables. But...

∫(dx)/(eˆx + eˆ(-x))=∫(eˆx)/(1 + eˆ2x) t=eˆx x=ln (t) (dt)/(dx)=t => dx=1/t dt ∫t/(tˆ2 + 1) * 1/t dt => ∫1/(tˆ2 + 1) dt Yeah! I solved it. You're right Dick, it isn't wrong at all. I just misthough there. The next phase is using a formula ∫1/(xˆ2 + 1) dx = arctan x + C So the...

[SOLVED] Integrating with Change of variables -method Homework Statement Solve by "Change of variables"-method ∫(dx)/(eˆx + eˆ(-x)) Homework Equations ∫f(x)dx=∫f(x(t))*x'(t)dt The Attempt at a Solution ∫(dx)/(eˆx + eˆ(-x))=∫(eˆx)/(1 + eˆ2x) t=eˆx x=ln...