这道数学题怎么做啊(前面的不定积分符号我就不写了,用换元积分法做)
1.(3-2x)^3 dx
2.dx/(1-2x)
3.dx/((xInx)*(In(Inx)))
4.xe^-ex^2 dx
5.dx/((x+1)*(x-2))
参考答案:1.∫(3-2x)^3 dx =(3-2x=y)=-(1/2)∫ydy=
=-(1/4)(y^2)+c=-(1/4)[(3-2x)^2]+c
2.∫dx/(1-2x)=(1-2x=y)=-(1/2)∫dy/y=
=-(1/2)ln|y|+c=-(1/2)ln|1-2x|+c
3.∫dx/{(xlnx)*[ln(lnx)]}=
=(lnx=y)=∫(e^y)dy/[(e^y)y(lny)=
=∫dy/ylny=(lny=u)=∫(e^u)du/(e^u)u=
=∫du/u=lnu+c=
=lnlny+c=lnlnlnx+c
4.没理解题目，该加括号的地方加上括号.
5.∫dx/[(x+1)*(x-2)]=
=-(1/3)∫dx[1/(x+1)-1/(x-2)]=
=-(1/3)[∫dx/(x+1)-∫dx/(x-2)=
=-(1/3)[ln|x+1|-ln|x-2|]+c=
=-(1/3)ln|(x+1)/(x-2)|+c