math: clarify substitute rule and provide general form

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eggy 2021-02-05 20:36:40 -05:00
parent 4917f30e18
commit 55e0865862

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@ -56,7 +56,11 @@ $$\int f(x)dx=F(x)+C$$
### Substitution rule
Similar to limit evaluation, the substitution of complex expressions involving $x$ and $dx$ with $u$ and $du$ can be done.
Similar to limit evaluation, the substitution of complex expressions involving $x$ and $dx$ with $u$ and $du$ is generally used to work with the chain rule.
$$
u=g(x) \\
\int f(g(s))\cdot g´(x)\cdot dx = \int f(u)\cdot du
$$
??? example
To solve $\int (x\sqrt{x-1})dx$: