How do you find the integral of (x^3 + 1) lnxdx(x3+1)lnxdx?

1 Answer
Lucy
Apr 30, 2018

(x^4/4+x)(In x)-x^4/16+x+C(x44+x)(Inx)−x416+x+C

Explanation:

Let u= In xInx
And dv=x^3+1x3+1 SO v=(x^4/4+x) (x44+x)

Integration by parts is given by = vu-intv duvu−∫vdu

int (x^3+1) In x dx∫(x3+1)Inxdx = (x^4/4+x)(In x)-int (x)(x^3/4+1)times1/x dx(x44+x)(Inx)−∫(x)(x34+1)×1xdx

=(x^4/4+x)(In x)-int (x^3/4+1) dx(x44+x)(Inx)−∫(x34+1)dx

=(x^4/4+x)(In x)-x^4/16+x+C(x44+x)(Inx)−x416+x+C

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