计算下列不定积分：1.∫(ln^3x/x)dx 2.∫[(sin1/x)/x^2]dx 3.∫[(x-1)e^x]dx 4.∫(x^2lnx)dx

1.∫(ln^3x/x)dx =∫ln^3xdlnx =ln^4x/4 +C2.∫[(sin1/x)/x^2]dx =-∫sin1/xd(1/x)=cos(1/x)+c3.∫[(x-1)e^x]dx=∫xe^xdx-∫e^xdx=[xe^x-∫e^xdx]-∫e^xdx=(x-2)e^x+c4.∫(x^2lnx)dx=1/3∫lnxdx^3=1/3(x^3lnx-∫x^3d...