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Integration by parts

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  1. Evaluate: ∫xcos⁡xdx\smallint x\cos x{d}x
    Topic Notes
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    In this section, we will learn how to integrate a product of two functions using integration by parts. This technique requires you to choose which function is substituted as "u", and which function is substituted as "dv". We will also take a look at two special cases. The first case is integrating a function which seems to not be a product of two functions. However, we see that we can actually have a product of two functions if we set "dv" as "dx". The second special case involves using integration by parts several times to get the answer.
    Integration by parts: ∫udv=uv−∫vdu\smallint u{d}v = uv - \smallint v{d}u
    *strategy: choose u = f(x) to be a function that becomes simpler when differentiated.