Page 718 - Handbook Of Integral Equations

√
x x
2
2
5. arccos dx = x arccos – a – x .
a a

x x x
2 2 √
2
2
6. arccos dx = x arccos – 2x – 2 a – x arccos .
a a a
√
x 1 2 2 x x
2
2
7. x arccos dx = (2x – a ) arccos – a – x .
a 4 a 4
x x x 1 2 2
3 √
2
2
2
8. x arccos dx = arccos – (x +2a ) a – x .
a 3 a 9
x x a 2 2

9. arctan dx = x arctan – ln(a + x ).
a a 2

x 1 2 2 x ax
10. x arctan dx = (x + a ) arctan – .
a 2 a 2
x x 3 x ax 2 a 3
2
2
2
11. x arctan dx = arctan – + ln(a + x ).
a 3 a 6 6
x x a 2 2

12. arccot dx = x arccot + ln(a + x ).
a a 2
x 1 2 2 x ax

13. x arccot dx = (x + a ) arccot + .
a 2 a 2
x x 3 x ax 2 a 3
2
2
2
14. x arccot dx = arccot + – ln(a + x ).
a 3 a 6 6
•
References for Supplement 2: H. B. Dwight (1961), I. S. Gradshteyn and I. M. Ryzhik (1980), A. P. Prudnikov,
Yu. A. Brychkov, and O. I. Marichev (1986, 1988).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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