✔ 最佳答案
1.
∫ x/(xlnx) dx
=∫1/(lnx) dx
=In|In x|+C
2.
∫ x/[x(lnx)^5] dx
=∫ 1/[(lnx)^5] dx
=∫ (In x)^-5 dx
=-025(In x)^-4 +C
3.
I=∫ x^2[(2x+3)^(1/3)] dx
設u=2x+3
x=(u-3)/2
du=2dx
du/2=dx
I=0.5∫ [(u-3)/2]^2[u^(1/3)] du
I=0.5(0.25)∫ (u^2 -6u+3)[u^(1/3)] du
I=0.125∫ (u^7/3 -6u^4/3 +3u^1/3)du
I=0.125[0.3u^10/3 -(18/7)(u^7/3) +(9/4)u^(2/3)]+C
I=0.375(2x+3)^(10/3) -(9/28)(2x+3)^(7/3) +0.28125(2x+3)^(2/3)+C