0.10: Sustitución
- Page ID
- 119252
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Se pueden integrar funciones más complicadas usando la regla de cadena. Desde
\[\frac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x),\nonumber \]
tenemos
\[\int f'(g(x))\cdot g'(x)dx=f(g(x))+c.\nonumber \]
Esta fórmula de integración suele ser implementada por dejar\(y = g(x)\). Entonces uno escribe\(dy = g'(x)dx\) para obtener
\[\begin{aligned} \int f'(g(x))g'(x)dx&=\int f'(y)dy \\ &=f(y)+c \\ &=f(g(x))+c.\end{aligned} \nonumber \]