Question

积分∫ln^2xdx

Answer 1

采用分部积分法：
∫ln�0�5xdx
=xln�0�5x - ∫x * 2lnx * 1/x dx
=xln�0�5x - 2xlnx + 2∫x * 1/x dx
=xln�0�5x - 2xlnx + 2x + C

Answer 2

∫ln^2xdx=∫ln^2xd1/2x^2=1/2x^2·ln^2x-∫xlnxdx=ln^2x·1/2x^2-∫lnxd1/2x^2=1/2x^2lnx^2-1/2x^2lnx+1/4x^2+c

Answer 3

原式=ln�0�5x+(2lnx*1/x）=ln�0�5x+2lnx/x
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