Optimal. Leaf size=22 \[ \text{Int}\left (\left (a+b x^4\right )^p \left (c+e x^2\right )^q,x\right ) \]
[Out]
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Rubi [A] time = 0.0230109, 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. \[ \text{Int}\left (\left (c+e x^2\right )^q \left (a+b x^4\right )^p,x\right ) \]
Verification is Not applicable to the result.
[In] Int[(c + e*x^2)^q*(a + b*x^4)^p,x]
[Out]
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Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \left (a + b x^{4}\right )^{p} \left (c + e x^{2}\right )^{q}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x**2+c)**q*(b*x**4+a)**p,x)
[Out]
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Mathematica [A] time = 0.0805122, size = 0, normalized size = 0. \[ \int \left (c+e x^2\right )^q \left (a+b x^4\right )^p \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(c + e*x^2)^q*(a + b*x^4)^p,x]
[Out]
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Maple [A] time = 0.117, size = 0, normalized size = 0. \[ \int \left ( e{x}^{2}+c \right ) ^{q} \left ( b{x}^{4}+a \right ) ^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x^2+c)^q*(b*x^4+a)^p,x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int{\left (b x^{4} + a\right )}^{p}{\left (e x^{2} + c\right )}^{q}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^p*(e*x^2 + c)^q,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (b x^{4} + a\right )}^{p}{\left (e x^{2} + c\right )}^{q}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^p*(e*x^2 + c)^q,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((e*x**2+c)**q*(b*x**4+a)**p,x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int{\left (b x^{4} + a\right )}^{p}{\left (e x^{2} + c\right )}^{q}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^p*(e*x^2 + c)^q,x, algorithm="giac")
[Out]