someone explain to me why the integral of
[eqn]6/x^3[/eqn] is NOT 6lnx^3, therefore 18lnx
>>8157190
Because it's -3/x^2. Why would it be something else?
think of it as 6*x^(-3)
>>8157190
>18lnx
Because the derivative of that shit is literally 18/x
This is why if you don't think of integrals completely in terms of anti derivatives you are bound to end up at Mc Donald's sucking dick at the playground.
>>8157239
so 1/x^3
is not lnx^3
>>8157241
No, nor is 1/(x^3) the derivative of ln(x^3) . Chain rule, nigger.
>>8157241
No it isn't. Not even close, really.
This is what happens when you embrace the
>not without my formula sheet
mentality instead of looking at the bigger picture.
>>8157246
Different anon here, I was a plug and chug calc student and I never had any problem using the chain rule so I'm not entirely sure what you mean.
Can't be assed to use LaTeX rn, so I did it on a sketchpad. Sorry, it's a bit hard to follow, but I used a fairly basic by-parts method.
>>8157305
Actually, I don't know why I used by-parts. Reverse power-rule can be used in all cases except when n = -1 and it's much faster in this case.
>>8157305
that's what I was thinking lol
>>8157305
WHY
[[integral of 6/x^(3) dx]] is of the form {{integral of cx^n dx]] which is always [[(c/n+1)x^(n+1) + C]].
>>8157190
>>8157190
because
[math] \displaystyle
\frac{d}{dx}(-3x^{-2}) = 6x^{-3}
[/math]
