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    Integration by parts

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    34.8 (a) Use integration by parts to evaluate
    1
    ∫ xּarctan x dx.
    0

    Hint: let u(x) = arctan x, so that u′(x) = 1/(1+x2).

    (b) If you used v(x) = x2/2 in part (a), do the computation again with v(x) = (x2+1)/2. This interesting example is taken from J. L. Borman[6].

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    https://brainmass.com/math/integrals/integration-parts-31263

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    This shows how to use integration by parts with an arctan integral.

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