U-substitution is for functions that can be written as the product of another function and its derivative. $$\int u du$$ Integration by parts is for functions that can be written as the product …

Jan 24, 2021 · How do I pick the right "u" for u substitution and when do I know I need to use it? Ask Question Asked 4 years, 9 months ago Modified 4 years, 9 months ago

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I don't feel qualified to give a full answer, but what's going on is some deep theorems with strong hypotheses, involving pushforward measures for Lebesgue integrals, or more simply a …

Feb 8, 2024 · u-substitution of indefinite integrals without algebraically manipulating differentials Ask Question Asked 1 year, 8 months ago Modified 1 year, 5 months ago

I've highlighted the part I don't understand in red. Why do we change the limits of integration here? What difference does it make? Source of Quotation: Calculus: Early Transcendentals, …

The substitution rule is always valid, regardless of the substitution made (so long as it is well defined). This is because the theorem that introduces substitutions effectively states "integral …

Solving improper integrals and u-substitution on infinite series convergent tests Ask Question Asked 13 years, 2 months ago Modified 13 years, 2 months ago

Dec 4, 2023 · Substitution in double integrals. When can I substitute the same way as in one-variable integrals, and when do I need to use the jacobian?

Sep 15, 2014 · As stated in many calculus textbooks (and ProofWiki),† the Substitution Rule (for the indefinite integral) is wrong. It is usually stated as: $$\int f \left ( {g \left ( {x}\right)}\right) g' …