5.5 The Substitution Rule/21

Failed to parse (syntax error): {\displaystyle \int \frac{\cos{(\sqrt{t})}}{\sqrt{t}}dt \ = \ \int \sqrt{u}du \\[2ex] }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} & \int\frac{\left(\ln(x)\right)^2}{x}dx \ = \ \int u^2du \\[2ex] & = \ \frac{u^{2+1}}{2+1}du \ = \ \frac{1}{3}u^3+C \\[2ex] & u=\ln(x) \\ & du=\frac{1}{x}dx \\ & = \ \frac{1}{3}(\ln(x))^3+C \end{align} }