R roxxar New member Joined Nov 30, 2013 Messages 1 Nov 30, 2013 #1 how do i start with this integral? function: f(x) = x*sin(1/x) F(x) =?
R Romsek Senior Member Joined Nov 16, 2013 Messages 1,361 Nov 30, 2013 #2 roxxar said: how do i start with this integral? function: f(x) = x*sin(1/x) F(x) =? Click to expand... I think I'd make a substitution u = 1/x. Then follow through using integration by parts. I don't think you'll be able to find a fully closed form though. The answer is 1/2 x Cos[1/x] + 1/2 x2 Sin[1/x] + 1/2 SinIntegral[1/x] Where SinIntegral[x] is the antiderivative of Sin[x]/x Last edited: Nov 30, 2013
roxxar said: how do i start with this integral? function: f(x) = x*sin(1/x) F(x) =? Click to expand... I think I'd make a substitution u = 1/x. Then follow through using integration by parts. I don't think you'll be able to find a fully closed form though. The answer is 1/2 x Cos[1/x] + 1/2 x2 Sin[1/x] + 1/2 SinIntegral[1/x] Where SinIntegral[x] is the antiderivative of Sin[x]/x
