Integration by Substitution/Primitive/Also presented as

Integration by Substitution: Also presented as

The rule of Integration by Substitution can also be seen in the form:

$\ds \int \map f x = \int \map \phi u \dfrac {\d x} {\d u} \rd u$

and:

$\ds \int \map F {\map \phi x} \rd x = \int \dfrac {\map F u} {\map {f'} x} \rd u$

where $x = \map \phi u$.


Sources

  • 1960: Margaret M. Gow: A Course in Pure Mathematics ... (previous) ... (next): Chapter $10$: Integration: $10.4$. Standard integrals: General Rules: $\text {V}$.
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