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rf:= (3*a*b**2-5*a**2*b)/(a**4-2)
2 2
3a b - 5a b
------------
4
a - 2
Type: Fraction Polynomial Integer
integrate(rf, a)
+--------------------------------------+
| 2 2 4
(\|- 12%%G1 - 8%%G0 %%G1 - 12%%G0 + 9b - 2%%G1 - 2%%G0)
*
log
(24a %%G1 + 24a %%G0 - 60b - 50a)
*
+--------------------------------------+
| 2 2 4
\|- 12%%G1 - 8%%G0 %%G1 - 12%%G0 + 9b
+
2 2
48a %%G1 + (120b + 100a)%%G1 + 48a %%G0 + (120b + 100a)%%G0
+
4
- 27a b - 250b
+
+--------------------------------------+
| 2 2 4
(- \|- 12%%G1 - 8%%G0 %%G1 - 12%%G0 + 9b - 2%%G1 - 2%%G0)
*
log
(24a %%G1 + 24a %%G0 - 60b - 50a)
*
+--------------------------------------+
| 2 2 4
\|- 12%%G1 - 8%%G0 %%G1 - 12%%G0 + 9b
+
2 2
- 48a %%G1 + (- 120b - 100a)%%G1 - 48a %%G0
+
4
(- 120b - 100a)%%G0 + 27a b + 250b
+
2 4
4%%G1 log(96a %%G1 + (240b + 200a)%%G1 - 27a b + 250b)
+
2 4
4%%G0 log(96a %%G0 + (240b + 200a)%%G0 - 27a b + 250b)
/
4
Type: Union(Expression Integer,...)
(10*x**2-11*x-6)/(x**3-x**2-2*x)
2
10x - 11x - 6
--------------
3 2
x - x - 2x
Type: Fraction Polynomial Integer
padicFraction( _
partialFraction(numerator(
factor(denominator(
Factored UnivariatePolynomial(x, Fraction Integer)))
3 2 5
- + ----- + -----
x x - 2 x + 1
Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)