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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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4.5 Inverse Trigonometric Functions

4.51 Inverse trigonometric functions

4.511

0arccotpx?arccot?qx?dx=π2{1pln(1+pq)+1qln(1+qp)}

si1340_e  BI (77)(8)

[p > 0, q > 0]

4.512

0πarctan(cosx)dx=0

si1341_e  BI (345)(1)

4.52 Combinations of arcsines, arccosines, and powers

4.521

1. 

01arcsinxxdx=π2ln2

si1342_e  FI II 614, 623

2. 

01arccosx1±xdx=π2ln2+2G

si1343_e  BI (231)(7, ...

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