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10 cards from this deck
Product of two functions unrelated by differentiation
∫udvdxdx=uv−∫vdudxdx\int u \frac{dv}{dx} dx = uv - \int v \frac{du}{dx} dx∫udxdvdx=uv−∫vdxdudx
Product rule: (uv)′=uv′+vu′(uv)' = uv' + vu'(uv)′=uv′+vu′
−xcosx+sinx+c-x \cos x + \sin x + c−xcosx+sinx+c
xex−ex+Cxe^x - e^x + Cxex−ex+C
No, use integration by parts
uuu (not dvdx\frac{dv}{dx}dxdv)
xlnx−x+cx \ln x - x + cxlnx−x+c
x22lnx−x24+c\frac{x^2}{2}\ln x - \frac{x^2}{4} + c2x2lnx−4x2+c
Substitution
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