Can someone help me prove that \[\displaystyle \int f(x)\left (\frac{dx}{dt}\right )dt = \int f(x) dx \]
What I would do is treat the differentials as fractions and just cancel the \(dt\) on numerator and denominator. However, I feel that it is cheating somehow. Is there a "formal" proof for this?

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I like the cheating method :) Makes life easy. But I can't help you on the real proof..

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