3.30 \(\int \frac{x^3 \left (A+B x+C x^2\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)

Optimal. Leaf size=347 \[ -\frac{(A b-2 a C) \tanh ^{-1}\left (\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{3/2}}+\frac{x^2 \left (2 a c C+A b c+b^2 (-C)\right )+a (2 A c-b C)}{2 c \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac{B x \left (2 a+b x^2\right )}{2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac{B \left (b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right )}{2 \sqrt{2} \sqrt{c} \left (b^2-4 a c\right ) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{B \left (b \sqrt{b^2-4 a c}+4 a c+b^2\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right )}{2 \sqrt{2} \sqrt{c} \left (b^2-4 a c\right )^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}} \]

[Out]

(B*x*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (a*(2*A*c - b*C) + (
A*b*c - b^2*C + 2*a*c*C)*x^2)/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (B*(b -
(b^2 + 4*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 -
4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (B*(b^
2 + 4*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 -
4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) -
((A*b - 2*a*C)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)

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Rubi [A]  time = 1.36615, antiderivative size = 347, normalized size of antiderivative = 1., number of steps used = 10, number of rules used = 9, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.321 \[ -\frac{(A b-2 a C) \tanh ^{-1}\left (\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{3/2}}+\frac{x^2 \left (2 a c C+A b c+b^2 (-C)\right )+a (2 A c-b C)}{2 c \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac{B x \left (2 a+b x^2\right )}{2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac{B \left (b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right )}{2 \sqrt{2} \sqrt{c} \left (b^2-4 a c\right ) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{B \left (b \sqrt{b^2-4 a c}+4 a c+b^2\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right )}{2 \sqrt{2} \sqrt{c} \left (b^2-4 a c\right )^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}} \]

Antiderivative was successfully verified.

[In]  Int[(x^3*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4)^2,x]

[Out]

(B*x*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (a*(2*A*c - b*C) + (
A*b*c - b^2*C + 2*a*c*C)*x^2)/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (B*(b -
(b^2 + 4*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 -
4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (B*(b^
2 + 4*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 -
4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) -
((A*b - 2*a*C)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)

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Rubi in Sympy [A]  time = 136.213, size = 289, normalized size = 0.83 \[ \frac{\sqrt{2} B \left (4 a c + b^{2} + b \sqrt{- 4 a c + b^{2}}\right ) \operatorname{atan}{\left (\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b + \sqrt{- 4 a c + b^{2}}}} \right )}}{4 \sqrt{c} \sqrt{b + \sqrt{- 4 a c + b^{2}}} \left (- 4 a c + b^{2}\right )^{\frac{3}{2}}} - \frac{\sqrt{2} B \left (4 a c + b^{2} - b \sqrt{- 4 a c + b^{2}}\right ) \operatorname{atan}{\left (\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b - \sqrt{- 4 a c + b^{2}}}} \right )}}{4 \sqrt{c} \sqrt{b - \sqrt{- 4 a c + b^{2}}} \left (- 4 a c + b^{2}\right )^{\frac{3}{2}}} + \frac{x \left (2 B a + B b x^{2} - x^{3} \left (2 A c - C b\right ) - x \left (A b - 2 C a\right )\right )}{2 \left (- 4 a c + b^{2}\right ) \left (a + b x^{2} + c x^{4}\right )} - \frac{\left (A b - 2 C a\right ) \operatorname{atanh}{\left (\frac{b + 2 c x^{2}}{\sqrt{- 4 a c + b^{2}}} \right )}}{\left (- 4 a c + b^{2}\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**3*(C*x**2+B*x+A)/(c*x**4+b*x**2+a)**2,x)

[Out]

sqrt(2)*B*(4*a*c + b**2 + b*sqrt(-4*a*c + b**2))*atan(sqrt(2)*sqrt(c)*x/sqrt(b +
sqrt(-4*a*c + b**2)))/(4*sqrt(c)*sqrt(b + sqrt(-4*a*c + b**2))*(-4*a*c + b**2)*
*(3/2)) - sqrt(2)*B*(4*a*c + b**2 - b*sqrt(-4*a*c + b**2))*atan(sqrt(2)*sqrt(c)*
x/sqrt(b - sqrt(-4*a*c + b**2)))/(4*sqrt(c)*sqrt(b - sqrt(-4*a*c + b**2))*(-4*a*
c + b**2)**(3/2)) + x*(2*B*a + B*b*x**2 - x**3*(2*A*c - C*b) - x*(A*b - 2*C*a))/
(2*(-4*a*c + b**2)*(a + b*x**2 + c*x**4)) - (A*b - 2*C*a)*atanh((b + 2*c*x**2)/s
qrt(-4*a*c + b**2))/(-4*a*c + b**2)**(3/2)

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Mathematica [A]  time = 1.84205, size = 358, normalized size = 1.03 \[ \frac{1}{4} \left (-\frac{2 \left (a (2 A c-b C+2 c x (B+C x))+b x^2 (A c-b C+B c x)\right )}{c \left (4 a c-b^2\right ) \left (a+b x^2+c x^4\right )}+\frac{2 (A b-2 a C) \log \left (\sqrt{b^2-4 a c}-b-2 c x^2\right )}{\left (b^2-4 a c\right )^{3/2}}-\frac{2 (A b-2 a C) \log \left (\sqrt{b^2-4 a c}+b+2 c x^2\right )}{\left (b^2-4 a c\right )^{3/2}}+\frac{\sqrt{2} B \left (b \sqrt{b^2-4 a c}-4 a c-b^2\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right )}{\sqrt{c} \left (b^2-4 a c\right )^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} B \left (b \sqrt{b^2-4 a c}+4 a c+b^2\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right )}{\sqrt{c} \left (b^2-4 a c\right )^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[(x^3*(A + B*x + C*x^2))/(a + b*x^2 + c*x^4)^2,x]

[Out]

((-2*(b*x^2*(A*c - b*C + B*c*x) + a*(2*A*c - b*C + 2*c*x*(B + C*x))))/(c*(-b^2 +
4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[2]*B*(-b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])*A
rcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[c]*(b^2 - 4*a*c)^(
3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*B*(b^2 + 4*a*c + b*Sqrt[b^2 - 4*a*c
])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[c]*(b^2 - 4*a*
c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (2*(A*b - 2*a*C)*Log[-b + Sqrt[b^2 - 4*a
*c] - 2*c*x^2])/(b^2 - 4*a*c)^(3/2) - (2*(A*b - 2*a*C)*Log[b + Sqrt[b^2 - 4*a*c]
+ 2*c*x^2])/(b^2 - 4*a*c)^(3/2))/4

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Maple [B]  time = 0.101, size = 3041, normalized size = 8.8 \[ \text{output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x)

[Out]

(-1/2*b*B/(4*a*c-b^2)*x^3-1/2*(A*b*c+2*C*a*c-C*b^2)/(4*a*c-b^2)/c*x^2-a*B/(4*a*c
-b^2)*x-1/2*a*(2*A*c-C*b)/c/(4*a*c-b^2))/(c*x^4+b*x^2+a)+c/(4*a*c-b^2)/(16*a^2*c
^2-8*a*b^2*c+b^4)/(-8*a*c^2+2*b^2*c)*ln(-8*x^2*a*c^2+2*x^2*b^2*c-4*a*b*c+b^3+(-(
4*a*c-b^2)^3)^(1/2))*A*(-64*a^3*c^3+48*a^2*b^2*c^2-12*a*b^4*c+b^6)^(1/2)*b^3+c/(
4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)/(8*a*c^2-2*b^2*c)*ln(8*x^2*a*c^2-2*x^2*b^2
*c+4*a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2))*A*(-64*a^3*c^3+48*a^2*b^2*c^2-12*a*b^4*c+
b^6)^(1/2)*b^3+8/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)/(8*a*c^2-2*b^2*c)*ln(8*x
^2*a*c^2-2*x^2*b^2*c+4*a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2))*C*(-64*a^3*c^3+48*a^2*b
^2*c^2-12*a*b^4*c+b^6)^(1/2)*a^2*c^2-2*c/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)/
(8*a*c^2-2*b^2*c)*ln(8*x^2*a*c^2-2*x^2*b^2*c+4*a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2))
*C*(-64*a^3*c^3+48*a^2*b^2*c^2-12*a*b^4*c+b^6)^(1/2)*a*b^2-3*c/(4*a*c-b^2)/(16*a
^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((4*a*c-b^2)*c*(4*a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2)
))^(1/2)*arctan(1/2*(8*a*c^2-2*b^2*c)*x*2^(1/2)/((4*a*c-b^2)*c*(4*a*b*c-b^3+(-(4
*a*c-b^2)^3)^(1/2)))^(1/2))*B*a*b^5+1/4/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*2
^(1/2)/((4*a*c-b^2)*c*(4*a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2)))^(1/2)*arctan(1/2*(8*
a*c^2-2*b^2*c)*x*2^(1/2)/((4*a*c-b^2)*c*(4*a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2)))^(1
/2))*B*b^7+1/4/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-4*a*b*c+b^3+(-(
4*a*c-b^2)^3)^(1/2))*(4*a*c-b^2)*c)^(1/2)*arctanh(1/2*(-8*a*c^2+2*b^2*c)*x*2^(1/
2)/((-4*a*b*c+b^3+(-(4*a*c-b^2)^3)^(1/2))*(4*a*c-b^2)*c)^(1/2))*B*(-64*a^3*c^3+4
8*a^2*b^2*c^2-12*a*b^4*c+b^6)^(1/2)*b^4-4/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)
/(8*a*c^2-2*b^2*c)*ln(8*x^2*a*c^2-2*x^2*b^2*c+4*a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2)
)*A*(-64*a^3*c^3+48*a^2*b^2*c^2-12*a*b^4*c+b^6)^(1/2)*b*a*c^2+8/(4*a*c-b^2)/(16*
a^2*c^2-8*a*b^2*c+b^4)/(-8*a*c^2+2*b^2*c)*ln(-8*x^2*a*c^2+2*x^2*b^2*c-4*a*b*c+b^
3+(-(4*a*c-b^2)^3)^(1/2))*C*(-64*a^3*c^3+48*a^2*b^2*c^2-12*a*b^4*c+b^6)^(1/2)*a^
2*c^2-2*c/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)/(-8*a*c^2+2*b^2*c)*ln(-8*x^2*a*
c^2+2*x^2*b^2*c-4*a*b*c+b^3+(-(4*a*c-b^2)^3)^(1/2))*C*(-64*a^3*c^3+48*a^2*b^2*c^
2-12*a*b^4*c+b^6)^(1/2)*a*b^2-3*c/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)
/((-4*a*b*c+b^3+(-(4*a*c-b^2)^3)^(1/2))*(4*a*c-b^2)*c)^(1/2)*arctanh(1/2*(-8*a*c
^2+2*b^2*c)*x*2^(1/2)/((-4*a*b*c+b^3+(-(4*a*c-b^2)^3)^(1/2))*(4*a*c-b^2)*c)^(1/2
))*B*a*b^5+1/4/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-4*a*b*c+b^3+(-(
4*a*c-b^2)^3)^(1/2))*(4*a*c-b^2)*c)^(1/2)*arctanh(1/2*(-8*a*c^2+2*b^2*c)*x*2^(1/
2)/((-4*a*b*c+b^3+(-(4*a*c-b^2)^3)^(1/2))*(4*a*c-b^2)*c)^(1/2))*B*b^7-16*c^3/(4*
a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((4*a*c-b^2)*c*(4*a*b*c-b^3+(-(4*a*c
-b^2)^3)^(1/2)))^(1/2)*arctan(1/2*(8*a*c^2-2*b^2*c)*x*2^(1/2)/((4*a*c-b^2)*c*(4*
a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2)))^(1/2))*B*a^3*b+12*c^2/(4*a*c-b^2)/(16*a^2*c^2
-8*a*b^2*c+b^4)*2^(1/2)/((4*a*c-b^2)*c*(4*a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2)))^(1/
2)*arctan(1/2*(8*a*c^2-2*b^2*c)*x*2^(1/2)/((4*a*c-b^2)*c*(4*a*b*c-b^3+(-(4*a*c-b
^2)^3)^(1/2)))^(1/2))*B*a^2*b^3+4/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)
/((4*a*c-b^2)*c*(4*a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2)))^(1/2)*arctan(1/2*(8*a*c^2-
2*b^2*c)*x*2^(1/2)/((4*a*c-b^2)*c*(4*a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2)))^(1/2))*B
*(-64*a^3*c^3+48*a^2*b^2*c^2-12*a*b^4*c+b^6)^(1/2)*a^2*c^2-1/4/(4*a*c-b^2)/(16*a
^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((4*a*c-b^2)*c*(4*a*b*c-b^3+(-(4*a*c-b^2)^3)^(1/2)
))^(1/2)*arctan(1/2*(8*a*c^2-2*b^2*c)*x*2^(1/2)/((4*a*c-b^2)*c*(4*a*b*c-b^3+(-(4
*a*c-b^2)^3)^(1/2)))^(1/2))*B*(-64*a^3*c^3+48*a^2*b^2*c^2-12*a*b^4*c+b^6)^(1/2)*
b^4-4/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)/(-8*a*c^2+2*b^2*c)*ln(-8*x^2*a*c^2+
2*x^2*b^2*c-4*a*b*c+b^3+(-(4*a*c-b^2)^3)^(1/2))*A*(-64*a^3*c^3+48*a^2*b^2*c^2-12
*a*b^4*c+b^6)^(1/2)*b*a*c^2-16*c^3/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2
)/((-4*a*b*c+b^3+(-(4*a*c-b^2)^3)^(1/2))*(4*a*c-b^2)*c)^(1/2)*arctanh(1/2*(-8*a*
c^2+2*b^2*c)*x*2^(1/2)/((-4*a*b*c+b^3+(-(4*a*c-b^2)^3)^(1/2))*(4*a*c-b^2)*c)^(1/
2))*B*a^3*b+12*c^2/(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-4*a*b*c+b^3
+(-(4*a*c-b^2)^3)^(1/2))*(4*a*c-b^2)*c)^(1/2)*arctanh(1/2*(-8*a*c^2+2*b^2*c)*x*2
^(1/2)/((-4*a*b*c+b^3+(-(4*a*c-b^2)^3)^(1/2))*(4*a*c-b^2)*c)^(1/2))*B*a^2*b^3-4/
(4*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-4*a*b*c+b^3+(-(4*a*c-b^2)^3)^(
1/2))*(4*a*c-b^2)*c)^(1/2)*arctanh(1/2*(-8*a*c^2+2*b^2*c)*x*2^(1/2)/((-4*a*b*c+b
^3+(-(4*a*c-b^2)^3)^(1/2))*(4*a*c-b^2)*c)^(1/2))*B*(-64*a^3*c^3+48*a^2*b^2*c^2-1
2*a*b^4*c+b^6)^(1/2)*a^2*c^2

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \frac{B b c x^{3} + 2 \, B a c x - C a b + 2 \, A a c -{\left (C b^{2} -{\left (2 \, C a + A b\right )} c\right )} x^{2}}{2 \,{\left ({\left (b^{2} c^{2} - 4 \, a c^{3}\right )} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} +{\left (b^{3} c - 4 \, a b c^{2}\right )} x^{2}\right )}} + \frac{\int \frac{B b x^{2} - 2 \, B a - 2 \,{\left (2 \, C a - A b\right )} x}{c x^{4} + b x^{2} + a}\,{d x}}{2 \,{\left (b^{2} - 4 \, a c\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((C*x^2 + B*x + A)*x^3/(c*x^4 + b*x^2 + a)^2,x, algorithm="maxima")

[Out]

1/2*(B*b*c*x^3 + 2*B*a*c*x - C*a*b + 2*A*a*c - (C*b^2 - (2*C*a + A*b)*c)*x^2)/((
b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2) + 1/2*in
tegrate((B*b*x^2 - 2*B*a - 2*(2*C*a - A*b)*x)/(c*x^4 + b*x^2 + a), x)/(b^2 - 4*a
*c)

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: NotImplementedError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((C*x^2 + B*x + A)*x^3/(c*x^4 + b*x^2 + a)^2,x, algorithm="fricas")

[Out]

Exception raised: NotImplementedError

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3*(C*x**2+B*x+A)/(c*x**4+b*x**2+a)**2,x)

[Out]

Timed out

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GIAC/XCAS [F(-2)]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((C*x^2 + B*x + A)*x^3/(c*x^4 + b*x^2 + a)^2,x, algorithm="giac")

[Out]

Exception raised: TypeError