Table of Integrals, Series, and Products, 8th Edition

4.5 Inverse Trigonometric Functions

4.51 Inverse trigonometric functions

4.511

${\displaystyle {\int }_0^{\infty }\text{arc}\cot }px\text{?}\text{arc}\cot \text{?}qx\text{?}\text{d}x=\frac{\pi }{2}\left\{\frac{1}{p}ln\left(1+\frac{p}{q}\right)+\frac{1}{q}ln\left(1+\frac{q}{p}\right)\right\}$

  BI (77)(8)

[p > 0, q > 0]

4.512

${\displaystyle {\int }_0^{\pi }\text{arctan}\left(cosx\right)\text{d}x}=0$

  BI (345)(1)

4.52 Combinations of arcsines, arccosines, and powers

4.521

1. 

${\displaystyle {\int }_0^1\frac{\arcsin x}{x}}\text{d}x=\frac{\pi }{2}ln2$

  FI II 614, 623

2. 

${\displaystyle {\int }_0^1\frac{\arccos x}{1\pm x}}\text{d}x=\mp \frac{\pi }{2}ln2+2G$

  BI (231)(7, ...