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

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