How do you integrate #(x^4)(lnx)#?

1 Answer
Shwetank Mauria
Jul 26, 2016

#intlnx xxx^4dx=x^5/5(lnx-1/5)#

Explanation:

WE can use integration by parts #intudv=uv-intvdu#

Let #u=lnx# and #v=x^5/5#

Hence #du=dx/x# and #dv=x^4dx# and #intudv=uv=intvdu# is

#intlnx xxx^4dx=intudv=uv-intvdu#

= #x^5/5xxlnx-intx^5/5xxdx/x#

= #(lnx xx x^5)/5-1/5intx^4dx#

= #(lnx xx x^5)/5-x^5/25#

= #x^5/5(lnx-1/5)#

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