Integrate by parts ? x^3 ln x dx

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Answer 1 · 2018-04-10T09:18:54

#= x^4/4 ( ln x - 1/4) + C#

IBP: #int u \ dv = uv - int v \ du#

Here:

#int x^3 \ ln x \ dx = int d(x^4/4) \ ln x#

#= x^4/4 ln x - int x^4/4 \ d( ln x)#

#= x^4/4 ln x - int x^4/4 \ 1/x dx#

#= x^4/4 ln x - x^4/16 + C#

#= x^4/4 ( ln x - 1/4) + C#