原式=∫(2*2^x)*[(3²)^x]*[(4^x)/4]dx
=(1/2)∫(2*3²*4)^xdx
=(1/2)∫72^xdx
=[(1/2)/ln72]∫e^(xln72)d(xln72)
=[1/(2ln72)]e^(xln72)+C (C是积分常数)
=72^x/(2ln72)+C.