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[Hitman]

How do you integrate 1/2X????

Is it ln|2x|?

 

[7imz]

take the 1/2 out then integrate...

1/2*ln(x)

 

[Ecrofirt]

[removed the wrong one]

maybe 7ims is right? It's too late for me to think about integration. I think maybe you'd make u=x

u=x

dx=du/1

S=integral symbol

(1/2)S(du/u)

(1/2)ln|u| +c

(1/2)ln|x|+c

 

[7imz]

the thing is do we need to use substitution over here.... we're integrating w.r.t x so we can simple take the 1/2 out

1/2S1/x

1/2*ln(x)

at least that's how i remember it

 

[Ecrofirt]

yes, I know that's what you do.

I did it with u-substitution in case he's just beginning or something and that's the only way he knows to ln.

When we first learned it, the definition was: Sdu/u = ln|u| + C

so I just went more round-about so he could see that

 

[fallout]

Wait, why waste time with substitution on this? I could understand even if the function was something like, x^3 * sqrt(x^4 + 1), but for something like this, it really does seem like a bad idea to encourage someone to do it.

I mean, what's the difference between integrating 1 / (2 * x) and 1 / (2 * u)? S k * f(x) dx is just k * S f(x) dx, so you're just integrating 1 / x or 1 / u.