原式=∫(0~1)t³e^(2t)dt (令√x=t)
=e²/2-(3/2)∫(0~1)t²e^(2t)dt (应用分部积分法)
=e²/2-3e²/4+(3/2)∫(0~1)te^(2t)dt (应用分部积分法)
=-e²/4+3e²/4-(3/4)∫(0~1)e^(2t)dt (应用分部积分法)
=e²/2-(3/4)(e²/2-1/2)
=(e²+3)/8