How do you integrate #(5 ln(x))/x^(7)#?

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Answer 1 · 2018-05-13T17:07:31

The answer is #=-5/6lnx/x^6-5/(36x^6)+C#

#intuv'=uv-u'v#

The integral is

#I=int(5lnxdx)/x^7=5int(lnx)/x^7#

#u=lnx#, #=>#, #u'=1/x#

#v'=x^-7#, #=>#, #v=-1/(6x^6)#

Therefore,

#I=-5/6lnx/x^6+5/6int(dx)/x^7#

#=-5/6lnx/x^6-5/(36x^6)+C#