How do you evaluate the integral $int lnxdx$ from [1,e]?

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Answer 1 · 2016-12-27T06:56:16

The answer is $=1$

$intuv'dx=uv-intu'vdx$

Here,

$u=lnx$ , $=>$ , $u'=1/x$

$v'=1$ , $=>$ , $v=x$

Therefore,

$int_1 ^elnx=[xlnx]_1^e-int_1 ^e1/x*xdx$

$=[xlnx]_1^e-[x]_1^e$

$=e-0-e+1$

$=1$

How do you evaluate the integral int lnxdxint lnxdx from [1,e]?