Optimal. Leaf size=27 \[ \text{Int}\left (\frac{\left (a+b x^4+c x^2\right )^p}{\left (c+e x^2\right )^2},x\right ) \]
[Out]
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Rubi [A] time = 0.0283879, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{\left (a+c x^2+b x^4\right )^p}{\left (c+e x^2\right )^2},x\right ) \]
Verification is Not applicable to the result.
[In] Int[(a + c*x^2 + b*x^4)^p/(c + e*x^2)^2,x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**4+c*x**2+a)**p/(e*x**2+c)**2,x)
[Out]
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Mathematica [A] time = 0.0892746, size = 0, normalized size = 0. \[ \int \frac{\left (a+c x^2+b x^4\right )^p}{\left (c+e x^2\right )^2} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(a + c*x^2 + b*x^4)^p/(c + e*x^2)^2,x]
[Out]
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Maple [A] time = 0.077, size = 0, normalized size = 0. \[ \int{\frac{ \left ( b{x}^{4}+c{x}^{2}+a \right ) ^{p}}{ \left ( e{x}^{2}+c \right ) ^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^4+c*x^2+a)^p/(e*x^2+c)^2,x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{4} + c x^{2} + a\right )}^{p}}{{\left (e x^{2} + c\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + c*x^2 + a)^p/(e*x^2 + c)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (b x^{4} + c x^{2} + a\right )}^{p}}{e^{2} x^{4} + 2 \, c e x^{2} + c^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + c*x^2 + a)^p/(e*x^2 + c)^2,x, algorithm="fricas")
[Out]
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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((b*x**4+c*x**2+a)**p/(e*x**2+c)**2,x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{4} + c x^{2} + a\right )}^{p}}{{\left (e x^{2} + c\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + c*x^2 + a)^p/(e*x^2 + c)^2,x, algorithm="giac")
[Out]