integrate (lnx)^2 dx?

0 ⤊

integrate (lnx)^2 dx?

2007-02-22 12:50:55 · 2 answers · asked by ellejare 3 in Science & Mathematics ➔ Mathematics

2 answers

replace y = ln(x) => x = e^y, dx = (e^y)*dy, then you have integral((y^2)*(e^y)*dy) = [using partial integration] = (e^y)*(y^2 - 2*y +2) = x*(lnx^2 - 2*lnx +2).

2007-02-22 13:10:18 · answer #1 · answered by fernando_007 6 · 0⤊ 0⤋

Integrating by parts = x*(lnx)^2 -Int x*2lnx /x

The Int lnx*dx = xlnx-x
So Int (lnx)^2 = x*(lnx)^2 -2(xlnx-x)

2007-02-22 21:12:09 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋