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7.4: Tarea- u-sustitución
https://espanol.libretexts.org/Matematicas/Calculo_informal_con_aplicaciones_a_las_ciencias_biologicas_y_ambientales_(Seacrest)/07%3A_Reglas_para_la_integraci%C3%B3n/7.04%3A_Tarea-_u-sustituci%C3%B3n
$\begin{align*} & = \int (8x^3) u^2 \frac{1}{4x^3} du \\ & = \int 8 u^2 \frac{1}{4}du \\ & = 2 \int u^2du \end{align*}$ $2 \int u^2du = 2 \left( \frac{1}{3} u^3 \right ) + C = \frac{2}{3} u^3 + C$ ... $\begin{align*} & = \int (8x^3) u^2 \frac{1}{4x^3} du \\ & = \int 8 u^2 \frac{1}{4}du \\ & = 2 \int u^2du \end{align*}$ $2 \int u^2du = 2 \left( \frac{1}{3} u^3 \right ) + C = \frac{2}{3} u^3 + C$ $\begin{align*} & = \int (3x^2 - 1) e^u \frac{1}{3x^2 - 1} du \\ & = \int e^udu \end{align*}$ $\int (x^2 - \frac{1}{3}) e^{x^3 - x}dx$ $\int (e^x+ x)^5 (e^x+1)dx$ $\begin{align*} & = \int \frac{x}{u^3}\frac{1}{2x}du \\ & = \int \frac{1}{2u^3}du \\ & = \int \frac{1}{2}u^{-3}du \end{align*}$

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