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=\frac{\mathrm dx}x`, so the integral is


`\displaystyle7\int y\,\mathrm dy=\frac72y^2+C=\frac72(\ln x)^2+C`