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7.3: sustitución en U
https://espanol.libretexts.org/Matematicas/Calculo_informal_con_aplicaciones_a_las_ciencias_biologicas_y_ambientales_(Seacrest)/07%3A_Reglas_para_la_integraci%C3%B3n/7.03%3A_sustituci%C3%B3n_en_U
$\begin{align*} \int x (x^2 + 1)^7dx & = \int x u^7dx \\ & = \int x u^7 \left( \frac{du}{2x} \right) \\ & = \int \frac{x}{2x} u^7du \\ & = \int \frac{1}{2} u^7du \end{align*}$ \[\begin{align*} \int ... $\begin{align*} \int x (x^2 + 1)^7dx & = \int x u^7dx \\ & = \int x u^7 \left( \frac{du}{2x} \right) \\ & = \int \frac{x}{2x} u^7du \\ & = \int \frac{1}{2} u^7du \end{align*}$ $\begin{align*} \int \frac{8 (\ln(x))^3}{x}dx & = \int \frac{8 u^3}{x} \cdot \frac{du}{\frac{1}{x}} \\ & = \int \frac{8 u^3}{x \cdot \frac{1}{x}}du \\ & = \int \frac{8 u^3}{1}du \\ & = \int 8 u^3du \\ \end{align*}$

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