Page 708 - Handbook Of Integral Equations

1/2
dx 2 b a + bx
13. = – + ln .

2
(a – b x)x 3/2 a x a 3 a – bx 1/2
2
2 1/2
1/2 1/2
dx x 1 a + bx
14. = + ln .

2
2 1/2
2
2
2
2
3
(a – b x) x a (a – b x) 2a b a – bx 1/2
Integrals containing (a + bx) p/2 .
2

15. (a + bx) p/2 dx = (a + bx) (p+2)/2 .
b(p +2)

(p+4)/2 (p+2)/2
2 (a + bx) a(a + bx)
p/2
16. x(a + bx) dx = – .
b 2 p +4 p +2
2

2 (a + bx) (p+6)/2 2a(a + bx) (p+4)/2 a (a + bx) (p+2)/2
2
17. x (a + bx) p/2 dx = – + .
b 3 p +6 p +4 p +2
2 1/2
2
Integrals containing (x + a ) .
1 a 2
2
2 1/2
2
2 1/2
2 1/2
2

18. (x + a ) dx = x(a + x ) + ln x +(x + a ) .
2 2

1 2 2 3/2
2 1/2
2
19. x(x + a ) dx = (a + x ) .
3

1 2 2 3/2 3 2 2 2 1/2 3 4 2
2 3/2
2
20. (x + a ) dx = x(a + x ) + a x(a + x ) + a ln x +(x + a ) .

2 1/2
4 8 8
2 2 1/2
1 2 2 1/2 2 2 1/2 a +(x + a )
21. (x + a ) dx =(a + x ) – a ln .

x x
dx 2 2 1/2

22. √ =ln x +(x + a ) .
2
x + a 2
xdx 2 2 1/2

23. √ =(x + a ) .
2
x + a 2

2 –1/2
2
2
–2
2 –3/2
24. (x + a ) dx = a x(x + a ) .
2 1/2
2
Integrals containing (x – a ) .
2
1 2 2 1/2 a 2
2
2 1/2
25. (x – a ) dx = x(x – a ) – ln x +(x – a ) .
2 1/2

2 2
1 2 2 3/2

2 1/2
2
26. x(x – a ) dx = (x – a ) .
3
1 3 3
2
2
2 3/2
2
2 3/2
2
2
4
2 1/2

27. (x – a ) dx = x(x – a ) – a x(x – a ) + a ln x +(x – a ) .
2 1/2

4 8 8
1 2 2 1/2 2 2 1/2

28. (x – a ) dx =(x – a ) – a arccos .
a
x x
dx 2

29. √ =ln x +(x – a ) .
2 1/2

2
x – a 2

xdx 2 2 1/2
30. √ =(x – a ) .
2
x – a 2

2 –3/2
–2
2
2 –1/2
2
31. (x – a ) dx = –a x(x – a ) .
© 1998 by CRC Press LLC
© 1998 by CRC Press LLC
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