find the anti derivative of $$\sin \pi x-2\cos \frac{ x }{ 2 }$$

Question

anonymous · Answer

integrate it

anonymous · Answer

well for the first part i got $$-\frac{ \cos \pi x }{ \pi} $$  I believe that's correct.  but I'm having trouble with the second half

anonymous · Answer

would I use constant multiple rule and then just integrate cosine?

anonymous · Answer

+4sin(x/2)

anonymous · Answer

no minus sorry

anonymous · Answer

To avoid any confusion , go for x/2 = t... then convert dx into dt...

anonymous · Answer

Oh I see how it's done now. so you just did $$-2(\frac{ 1 }{ \frac{ 1 }{ 2 } })\sin \frac{ x }{ 2 } $$ correct?

anonymous · Answer

and you got -4sinx/2 correct?

anonymous · Answer

yes

anonymous · Answer

Yeah, that's like divide the {multiplied of 'x'} and do not change anything for 'added or subtracted'...
Like if there's cos(ax+ b)... then divide the (multiplied) a... and do not make changes for 'b' after integrating the cos term...