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Question Number 22051 by FilupS last updated on 10/Oct/17

I have recently seen a different notation  for integration, written as:                            ∫dxf(x)  e.g.        ∫dx(x+1)^2      Is this the same as:                            ∫f(x)dx  ⇒    =∫(x+1)^2 dx  ???

$$\mathrm{I}\:\mathrm{have}\:\mathrm{recently}\:\mathrm{seen}\:\mathrm{a}\:\mathrm{different}\:\mathrm{notation} \\ $$$$\mathrm{for}\:\mathrm{integration},\:\mathrm{written}\:\mathrm{as}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int{dxf}\left({x}\right) \\ $$$${e}.{g}. \\ $$$$\:\:\:\:\:\:\int{dx}\left({x}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\: \\ $$$$\mathrm{Is}\:\mathrm{this}\:\mathrm{the}\:\mathrm{same}\:\mathrm{as}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int{f}\left({x}\right){dx} \\ $$$$\Rightarrow\:\:\:\:=\int\left({x}+\mathrm{1}\right)^{\mathrm{2}} {dx} \\ $$$$??? \\ $$

Commented by Joel577 last updated on 10/Oct/17

I think it is same

$${I}\:{think}\:{it}\:{is}\:{same} \\ $$

Commented by Joel577 last updated on 10/Oct/17

or maybe (∫ dx) . f(x)

$${or}\:{maybe}\:\left(\int\:{dx}\right)\:.\:{f}\left({x}\right) \\ $$

Commented by FilupS last updated on 10/Oct/17

I don′t think so.  Without going into details,  they got something in form:  ∫dxf(x)=F(x)+c     but I am only aware of the form:  ∫f(x)dx=F(x)+c  to me: ∫dxf(x)=(∫dx)(f(x))  whereas: ∫f(x)dx≠(∫dx)(f(x)), because:  ∫f(x)dx=(F(x))(∫dx)

$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{so}. \\ $$$$\mathrm{Without}\:\mathrm{going}\:\mathrm{into}\:\mathrm{details}, \\ $$$$\mathrm{they}\:\mathrm{got}\:\mathrm{something}\:\mathrm{in}\:\mathrm{form}: \\ $$$$\int{dxf}\left({x}\right)={F}\left({x}\right)+{c} \\ $$$$\: \\ $$$$\mathrm{but}\:\mathrm{I}\:\mathrm{am}\:\mathrm{only}\:\mathrm{aware}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}: \\ $$$$\int{f}\left({x}\right){dx}={F}\left({x}\right)+{c} \\ $$$$\mathrm{to}\:\mathrm{me}:\:\int{dxf}\left({x}\right)=\left(\int{dx}\right)\left({f}\left({x}\right)\right) \\ $$$$\mathrm{whereas}:\:\int{f}\left({x}\right){dx}\neq\left(\int{dx}\right)\left({f}\left({x}\right)\right),\:\mathrm{because}: \\ $$$$\int{f}\left({x}\right){dx}=\left({F}\left({x}\right)\right)\left(\int{dx}\right) \\ $$

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