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How do you find the integral of #(x^3 + 1) lnxdx#?

1 Answer

Apr 30, 2018

#(x^4/4+x)(In x)-x^4/16+x+C#

Explanation:

Let u= #In x#
And dv=#x^3+1# SO v=#(x^4/4+x) #

Integration by parts is given by = #vu-intv du#

#int (x^3+1) In x dx# = #(x^4/4+x)(In x)-int (x)(x^3/4+1)times1/x dx#

=#(x^4/4+x)(In x)-int (x^3/4+1) dx#

=#(x^4/4+x)(In x)-x^4/16+x+C#

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