Well let's try...
Int x^3cos(x^2)
u = cos(x^2)
du = -2x sin (x^2)
dv = x^3
v = (x^4)/4
Int x^3cos(x^2) = (x^4cos(x^2))/4 + 1/2 Int x^5 sin (x^2)
u = sin(x^2)
du = 2x cos(x^2)
dv = x^5
v = (x^6)/6
Int x^5 sin (x^2) = (x^6sin(x^2))/6 - 1/3 Int x^7 cos (x^2)
Hmmm... Doesn't...
This has been posted before although I've come across it and got a different answer from https://www.physicsforums.com/archive/index.php/t-108378.html
x sinx cosx dx using the identity sin2x = 2sinxcosx
u = x
du = 1
dv = 1/2 sin 2x
v = -1/4 cos 2x
x sinx cosx dx = -1/4xcos2x - Int...