5.5 The Substitution Rule/17

Failed to parse (syntax error): {\displaystyle \int \frac{a+bx^2}}}{}dx }

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} u &=\5-3x du &= \frac{1}{x}dx \\[2ex] \end{align} }

${\begin{aligned}\int {\frac {\sin {(\ln {(x))}}}{x}}dx&=\int {\frac {1}{x}}\sin(\ln {(x)})dx=\int \left({\frac {1}{x}}dx\right)\sin {(\ln {(x)})}\\[2ex]&=\int (du)\sin {(u)}=\int \sin {(u)}du\\[2ex]&=-\cos {(u)}+C\\[2ex]&=-\cos {(\ln {(x)})}+C\end{aligned}}$