三道习题(不定积分)： dx/三次根号下3-5x dx/xlnxln(lnx) xln(x-1)dx

1,令³√(3-5x)=t,则x=(3-t³)/5,那么dx=-3t²/5dx
∫³√(3-5x) dx=∫t(-3t²/5) dt=-3/5 ∫t³dt=-3(t^4)/20 +C=-3(3-5x)^(4/3) /20+C
2,∫dx/[xlnxln(lnx)]
=∫d(lnx)/[lnxln(lnx)]
=∫d[ln(lnx)]/ln(lnx)
=ln[ln(lnx)]+C
3,∫xln(x-1) dx
=x²ln(x-1)/2-∫x²/[2(x-1)]dx
=x²ln(x-1)/2-1/2 ∫(x²-1+1)/(x-1)dx
=x²ln(x-1)/2-1/2 ∫[(x+1)+1/(x-1)]dx
x²ln(x-1)/2-1/2 [x²/2+x+ln(x-1)]+C