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Today's calculation of Integral 637

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August 20, 2010
calculusintegrationtrigonometrylogarithmscalculus computations

Problem Statement

For a non negative integer nn, set t In=∫0π4tan⁡nx dxI_n=\int_0^{\frac{\pi}{4}} \tan ^ n x\ dx to answer the following questions:
(1) Calculate In+2+In.I_{n+2}+I_n.
(2) Evaluate the values of I1, I2I_1,\ I_2 and I3.I_3.
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