Question

What is the antiderivative of `ln (x^2)`?

Answer 1

I would start by writing `ln(x^2)=2ln(x)`
So you get:
`int2ln(x)dx`
then I set:
`ln(x)=t` that gives:
`x=e^t` and:
`dx=e^tdt`
Substituting:
`int2ln(x)dx=2intte^tdt=` by Parts:
`=2[te^t-int1*e^tdt]=`
`=2[te^t-e^t]=`
`=2e^t(t-1)`
Substituting back to `x`:
`=2x[ln(x)-1]+c`