Question

微积分。。。

Answer 1

图

Answer 2

令x=t^6，则dx=6t^5dt
原式=∫6t^5/(t^3-t^2)dt
=∫6t^3/(t-1)dt
=6∫[(t^3-1)/(t-1)+1/(t-1)]dt
=6∫[t^2+t+1+1/(t-1)]dt
=2t^3+3t^2+6t+6ln|t-1|+C
=2√x+3x^(1/3)+6x^(1/6)+6ln|x^(1/6)-1|+C，其中C是任意常数