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10 cards from this deck
To integrate products of functions using uuu and dvdvdv.
It's the formula for integration by parts derivation.
∫udv=uv−∫vdu\int udv = uv - \int vdu∫udv=uv−∫vdu, where uuu and vvv are functions.
∫u dv=uv−∫v du\int u \, dv = uv - \int v \, du∫udv=uv−∫vdu
Let u=xu = xu=x, dv=sinx dxdv = \sin x \, dxdv=sinxdx.
xlnx−x+cx \ln x - x + cxlnx−x+c
Use integration by parts: u=x2u = x^2u=x2, dv=cosx dxdv = \cos x \, dxdv=cosxdx.
xex−ex+Cxe^x - e^x + Cxex−ex+C (correct result with integration)
Use it when replacing a variable simplifies the integral.
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