5.5 The Substitution Rule/21: Difference between revisions

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<math>
<math>
\int \frac{\cos{(\sqrt{t})}}{\sqrt{t}}dt  
\int \frac{\cos{(\sqrt{t})}}{\sqrt{t}} dt
 
\int\sqrt{u}du \\[2ex]
</math>
 
 
<math>
\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}
</math>

Revision as of 08:28, 7 September 2022

<math> \int \frac{\cos{(\sqrt{t})}}{\sqrt{t}} dt

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