2.8 Inverse Trigonometric Functions

2.81 Arcsines and arccosines

Assume a>0si2274_e

2.811 (arcsinxa)ndx=xk=0 n/2(1)k(n2k)(2k)!(arcsinxa)n2k+a2x2k=1 (n+1)/2(1)k1 (n2k1)(2k1)! (arcsinxa)n2k+1si2275_e

2.812 (arccosxa)ndx=xk=0 n/2(1)k(n2k)(2k)! (arccosxa)n2k+a2x2k=1 (n+1)/2(1)k( n2k1)(2k1)! (arccosxa)n2k+1si2276_e

2.813

1.11 

arcsinxadx=sign(a)[ x arcsinx| a|+a2x2]

2.9 

(arcsinxa)2dx=x(arcsinx| a|)2+2a2x2arcsinx| a|2x

3. 

(arcsin ...

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