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Section 8.2 Integration by parts
Objectives
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Reverse the Product Rule by choosing parts to differentiate and integrate.
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Use tabular integration for repeated applications.
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Identify cyclic integrals and solve them by recognizing reappearing terms.
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This is the “Anti-Product Rule”: if we can write our integrand in the form \(u\dd{v}\text{,}\) then we have
\begin{equation*}
\int u\dd{v}=uv-\int v\dd{u}
\end{equation*}
We want to choose \(u\) so it’s easy to differentiate and \(v\) so it’s easy to integrate.
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Tabular integration for IBP multiple times
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Cycle trick for
\(\DS\int \ee^{x}\cos x\dd{x}\)
