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It's the Reverse Chain Rule for simplifying integrals.
Choose a substitution uuu for part of the integrand.
Differentiate uuu to express dududu in terms of dxdxdx.
Rewrite the integral with uuu and dududu, replacing xxx terms.
Integrate with respect to uuu to solve the integral.
Substitute back the initial expression for uuu in xxx.
Only for functions where a part's derivative is present.
Products of functions that are differentiable.
When integrating rational functions with polynomial denominators.
sin2x+cos2x=1\sin^2 x + \cos^2 x = 1sin2x+cos2x=1, useful in integration.
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