How do you integrate $int sinxln(cosx)$ by integration by parts method?

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Answer 1 · 2016-08-11T10:08:36

$-cos(x)loge(cos(x))+cos(x) + C$

$d/(dx)(cos(x)log_e(cos(x)))=-sin(x) log_e(cos(x))-sin(x)$

so

$int sin(x) log_e(cos(x))dx =$
$= -int d/(dx)(cos(x)log_e(cos(x)))dx-int sin(x) dx =$
$= -cos(x)loge(cos(x))+cos(x) + C$

How do you integrate int sinxln(cosx)int sinxln(cosx) by integration by parts method?