Question

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

Answer 1

`(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`