9.3 “Table” Integration by PartsTable integration is an efficient way of integration by parts when multiple steps of integration by parts are required.The first example on pg 440 shows the process to be much easier when following these simple step by step rules.
1. Pick u and dv.UDVx2cos4x2. Differentiate u until 02x3. Integrate dv until the 0 in the u columnx4sin412x4cos161-0x4sin641-4. Multiply answer diagonally alternating signs+-+
=∫xdxxsin23UDV2x3sinx6x212x12-cosx-sinxcosxsinx0Solution:-2x3cosx+ 6x2sinx+ 12xcosx – 12sinx + C
=∫xdxexsinUDVexsinxSolution:ex-cosx-excosxex-sinx+ exsinxWhen the integral becomes the