Is reverse chain rule just integral of product of function and it's derivative? (1 Viewer)

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cossine

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You can think of it like that I guess

integral of sin(x)cos(x)
integral of (x+2)/ (x^2 + 4x)
 
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Drongoski

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Integrands which are derivatives(or constant multiples thereof) of composite functions are the ones usually handled by "integration by substitution". They often refer to reverse chain rule - but I've seldom seen how this reversal is achieved. Using my method, I can do the reversal of the chain rule step-by-step. But apart from a few, no one knows my method.
 
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medaspirant

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Drongoski said:
Integrands which are derivatives(or constant multiples thereof) of composite functions are the ones usually handled by "integration by substitution". They often refer to reverse chain rule - but I've seldom seen how this reversal is achieved. Using my method, I can do the reversal of the chain rule step-by-step. But apart from a few, no one knows my method.
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yep I also believe u sub is more straightforward in these cases but id also like to know how to use RCR
 
dan964

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Reverse chain rule would be basically a quick hand way of doing integration by substitution, by inspection. Generally its most useful for when you observe a composite function that you know get by differentiating using the chain rule. For the same reason differentiation by substitution is actually using the chain rule implicitly.
 
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