![]() It isn't really an exception, but you can sort of have leftover bits when you do integration by parts. ∫ cos (x²) dx is nightmarishly difficult (getting into something called Fresnel integrals). ∫ (x)∙cos(x²) dx is very easy to integrate but the very similar looking With integration, being close to a standard form is not good enough: you must have an exact match. So, the answer is, no, you cannot do u-substitution that way. And remember du is the derivative of whatever you called u, it is NOT just some notation. Where f(u) du is something you know how to integrate. ![]() The purpose of u substitution is to wind up with ∫ f(u) du A valid substitution, generally speaking, requires that ALL references to the original variable be replaced ESPECIALLY including its dx (or whatever the variable is). ![]() Sorry, that is ordinarily not a valid means of substitution.
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