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Black Book Advanced Problems in MathematicsMathematicsIndefinite and Definite Integration

Let I_n = _ -1 ^1 |x| ( 1 + x + x^2 2 + x^3 3 + + x^ 2n 2n ) dx . If _ n I_n can be expressed as rational p q in its lowest form, then find the value of pq(p+q) 10 .

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3

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