How do you integrate $int x^nlnx$ by integration by parts method?

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Answer 1 · 2016-07-20T23:26:26

$int x^n log_e x dx = x^{n+1}(((n+1)log_e x-1)/(n+1)^2)$

$d/(dx)(x^{n+1}log_e x) = (n+1)x^nlog_ex+x^n$

then

$(n+1)int x^n log_e x dx = x^{n+1}log_e x - 1/(n+1)x^{n+1}$

so

$int x^n log_e x dx = x^{n+1}(((n+1)log_e x-1)/(n+1)^2)$

How do you integrate int x^nlnxint x^nlnx by integration by parts method?