How to integrate cos^2(2x)?

Ayaana Buck 2021-03-12 Answered
How to integrate cos2(2x)?
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2k1enyvp
Answered 2021-03-13 Author has 94 answers
I = integral
Icos2(2x)dx=(12)Icos2(t)dt
2x=t,2dx=dt,dx=dt2
Icos2(t)dt=Icostcostdt
u=cost,du=sint
dv=costdt,v=sint
Icos2(t)dt=sintcost+Isin2(t)dt
Icos2(t)dt=sin(2t)2+I(1cos2(t))dt
Icos2(t)dt=sin(2t)2+IdtIcos2(t)dt
Icos2(t)dt+Icos2(t)dt=sin(2t)2
2Icos2(t)dt=sin(2t)2+t
Icos2(t)dt=sin(2t)4+t2
t=2x
=sin(4x)4+x
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