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4.5 Inverse Trigonometric Functions

4.51 Inverse trigonometric functions

4.511

${\int }_{0}^{\infty }\text{arc}\mathrm{cot}px\text{?}\text{arc}\mathrm{cot}\text{?}qx\text{?}\text{d}x=\frac{\pi }{2}\left\{\frac{1}{p}ln\left(1+\frac{p}{q}\right)+\frac{1}{q}ln\left(1+\frac{q}{p}\right)\right\}$

BI (77)(8)

[p > 0, q > 0]

4.512

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

BI (345)(1)

4.52 Combinations of arcsines, arccosines, and powers

4.521

1.

${\int }_{0}^{1}\frac{\mathrm{arcsin}x}{x}\text{d}x=\frac{\pi }{2}ln2$

FI II 614, 623

2.

${\int }_{0}^{1}\frac{\mathrm{arccos}x}{1±x}\text{d}x=\mp \frac{\pi }{2}ln2+2G$

BI (231)(7, ...

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