How do you integrate #ln(x^(1/3))#?

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Answer 1 · 2018-03-19T16:46:13

#1/3xlnx-1/3x+c#

#I=intln(x^(1/3))dx#

using the laws of logs

#I=int 1/3lnxdx#

#

we will integrate by parts

#I=1/3intlnxdx#

#I=intu(dv)/(dx)dx=uv-intv(du)/(dx)dx#

#u=lnx=>(du)/(dx)=1/x#

#(dv)/(dx)=1=>v=x#

#:.I=1/3[xlnx-intx xx 1/xdx]#

#I=1/3[xlnx-intdx]#

#=1/3[xlnx-x]+c#

#1/3xlnx-1/3x+c#