∫sin4xcos8xdx
=1/4∫sin4xcos8xd4x
=-1/4∫cos8xdcos4x
=-1/4∫[2(cos4x)^2-1]dcos4x
=-1/2∫(cos4x)^2dcos4x+1/4∫dcos4x
=-1/6(cos4x)^3+1/4cos4x+C
求一道不定积分题∫ sin4x*cos8x dx.
∫sin4xcos8xdx
=1/4∫sin4xcos8xd4x
=-1/4∫cos8xdcos4x
=-1/4∫[2(cos4x)^2-1]dcos4x
=-1/2∫(cos4x)^2dcos4x+1/4∫dcos4x
=-1/6(cos4x)^3+1/4cos4x+C