求助大佬们！这题怎么做？

f'(2x)=sin2x
(1/2) d/dx f(2x) = sin2x
f(2x) = 2∫ sin2x dx
= -cos2x +C
x=0
f(0) = -1+C
0=-1+C
C=1
ie
f(2x)= -cos2x +1
f(x)=-cosx +1