someone explain to me why the integral of [eqn]6/x^3[/eqn]

>>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.

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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]].

>>8157319
didnt read this comment

i am >>8157331
and obv, not when n=-1

lmao

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>>8157190

>>8157190
because
[math] \displaystyle
\frac{d}{dx}(-3x^{-2}) = 6x^{-3}
[/math]