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Relates InI_nInโ to Inโ1I_{n-1}Inโ1โ and/or Inโ2I_{n-2}Inโ2โ
โซudvdxdx=uvโโซvdudxdx\int u \frac{dv}{dx} dx = uv - \int v \frac{du}{dx} dxโซudxdvโdx=uvโโซvdxduโdx
Avoid repeated integration by parts; derive formula once
Recursive relationship
Part containing power nnn so power reduces when differentiated
Both definite and indefinite integrals
In=โnInโ1I_n = -nI_{n-1}Inโ=โnInโ1โ
In=nโ1nInโ2I_n = \frac{n-1}{n}I_{n-2}Inโ=nnโ1โInโ2โ
Reach I0I_0I0โ or I1I_1I1โ, evaluate directly, substitute back
Even powers reduce to I0I_0I0โ, odd powers to I1I_1I1โ
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