∫[x³/(9-x²)^(1/3)]dx【积分区间(1,2√2)】
=(1/2)∫[x²/(9-x²)^(1/3)]dx²
设y=(9-x²)^(1/3),x²=9-y³。
=(1/2)∫[(9-y³)/y]d(9-y³)【积分区间(2,1)】
=(-3/2)∫y(9-y³)dy
=(-3/2)[(9/2)y²-(1/5)y^5]【上限1,下限2】
=(-3/2){(9/2-1/5)-[(9/2)*2²-(1/5)*2^5]}
=(-3/20)[(45-2)-(45*4-2*32)]
=219/20
向左转|向右转过程写的比较简单,能看懂就行