Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

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

1 Answer

Jul 20, 2016

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

Explanation:

#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)#

Related questions

See all questions in Integration by Parts

Impact of this question

1736 views around the world

You can reuse this answer
Creative Commons License