Question

intergrate the following expression:
8sin5xcosx

Answer 1

\[\int\limits\limits 8\sin5xcosx dx\]\[=8\int\limits\limits \sin5xcosx dx\]\[= 8\int\limits (1/2) [\sin (5x+x) + \cos (5x-x) ]dx\]\[= 4\int\limits (\sin 6x + \cos 4x)dx\]\[= 4[(1/6)(-\cos6x) + 1/4 (\sin4x)]+C\]\[=\sin4x-2/3\cos6x+C\]
not sure it is correct since i just learnt it 2days ago :S