Question

#4. I'm not sure whether I should use u substation or basic antiderivative process.

Answer 1

$\displaystyle\int\frac{\ln x^7}x\,\mathrm dx=7\int\frac{\ln x}x\,\mathrm dx$

Set $y=\ln x$, recalling that $\mathrm dy=\dfrac{\mathrm dx}x$, so the integral is

$\displaystyle7\int y\,\mathrm dy=\dfrac72y^2+C=\dfrac72(\ln x)^2+C$