Integrate[ (3a b^2 - 5a^2 b)/(a^4 - 2), a ]
a
-5 b ArcTan[----]
1/4
2
----------------- -
1/4
2 2
3/4 2 3/4
(10 b - 3 2 b ) Log[-2 + 2 a]
1/4
8 2
3/4 2 3/4
(-10 b - 3 2 b ) Log[2 + 2 a]
1/4
8 2
2 2
3 b Log[2 + Sqrt[2] a ]
------------------------
4 Sqrt[2]
D[%,a]
2
-5 b 3 a b
----------------------- - ------------------ -
2 2
a 2 (2 + Sqrt[2] a )
2 Sqrt[2] (1 + -------)
Sqrt[2]
3/4 2 3/4 2
-10 b - 3 2 b 10 b - 3 2 b
---------------------- - -----------------------
3/4 3/4
4 Sqrt[2] (2 + 2 a) 4 Sqrt[2] (-2 + 2 a)
Simplify[%]
a b (-5 a + 3 b)
----------------
4
-2 + a
Apart[ (10x^2- 11x- 6)/(x^3- x^2- 2x)]
2 3 5
------ + - + -----
-2 + x x 1 + x