Question

evaluate each integral (lnx)^3 / (x) dx

Answer 1

since the d/dx of ln (x) is the the denominator the integral should look like this
\[\int\limits_{}^{}(\ln(x))^3d(\ln(x))=\int\limits_{}^{}(\ln(x))^3/xdx\]
so because d/dx(ln(x)) is sitting right there you can think of it as "u" so (ln(x))^3=u^3
INT u^3=u^4/4 since u=ln(x)
(ln(x))^4/4+C