Help with integration (1 Viewer)

[village_idiot69]

can anybody help me integrate sin(logex) with respect to x.

 

[KFunk]

Try integration by parts:

∫ sin(log_ex) dx = ∫ Sin(lnx).1 dx = ∫ uv' dx = uv - ∫ u'v

let v' = 1, v =x ------> u=sin(lnx) , u' = cos(lnx)/x

∫ sin(log_ex) dx
= xsin(lnx) - ∫ cos(lnx).x/x dx (apply the same method of int. by parts to ∫ cos(lnx) dx)
= xsin(lnx) - ( xcos(lnx) + ∫ sin(lnx).x/x dx)

hence
∫ sin(log_ex) dx = xsin(lnx) - xcos(lnx) - ∫ sin(log_ex) dx
2∫ sin(log_ex) dx = xsin(lnx) - xcos(lnx)
∫ sin(log_ex) dx = x/2.sin(log_ex) - x/2.cos(log_ex) + C

 

[village_idiot69]

thanks heaps...
i cant believe it, i was almost there, i gave up so close to the end.

 

[Dumsum]

PLUS C!!!!!!



Edit: all good