Take the integral:
3 integral1/3 x^4 log(x) dx
Factor out constants:
= integral x^4 log(x) dx
For the integrand x^4 log(x), integrate by parts, integral f dg = f g- integral g df, where
f = log(x), dg = x^4 dx, df = 1/x dx, g = x^5/5:
= 1/5 x^5 log(x)-1/5 integral x^4 dx
The integral of x^4 is x^5/5:
= 1/5 x^5 log(x)-x^5/25+constant
Which is equal to:
Answer: |= 1/25 x^5 (5 log(x)-1)+constant
