Evaluate : `int(logx)^(2)dx`.

1.	Evaluate : `int(logx)^(2)dx`.
Answer» Integrating by parts, taking `(logx)^(2)` as the first function and 1 as the second function, we get `int(logx)^(2)dx=int{(logx)^(2)1}dx` `=(logx)^(2)intdx-int{(d)/(dx)(logx)^(2)int1dx}dx` ]`=x(logx)^(2)-int((2logx)/(x)x)dx` `=x(logx)^(2)-2int(logx1)dx` `=x(logx)^(2)-2[(logx)intdx-int{(d)/(dx)(logx)intdx}dx]` `=x(logx)^(2)-2[xlogx-int(1)/(x)*xdx]` `=x(logx)^(2)-2xlogx+2x+C`.

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