Optimal. Leaf size=101 \[ x F_1\left (\frac{1}{4};3,-p;\frac{5}{4};x^4,-b x^4\right )+\frac{1}{7} x^7 F_1\left (\frac{7}{4};3,-p;\frac{11}{4};x^4,-b x^4\right )+\frac{3}{5} x^5 F_1\left (\frac{5}{4};3,-p;\frac{9}{4};x^4,-b x^4\right )+x^3 F_1\left (\frac{3}{4};3,-p;\frac{7}{4};x^4,-b x^4\right ) \]
[Out]
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Rubi [A] time = 0.269839, antiderivative size = 101, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 3, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.158 \[ x F_1\left (\frac{1}{4};3,-p;\frac{5}{4};x^4,-b x^4\right )+\frac{1}{7} x^7 F_1\left (\frac{7}{4};3,-p;\frac{11}{4};x^4,-b x^4\right )+\frac{3}{5} x^5 F_1\left (\frac{5}{4};3,-p;\frac{9}{4};x^4,-b x^4\right )+x^3 F_1\left (\frac{3}{4};3,-p;\frac{7}{4};x^4,-b x^4\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 + b*x^4)^p/(1 - x^2)^3,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+1)**p/(-x**2+1)**3,x)
[Out]
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Mathematica [A] time = 0.0852825, size = 0, normalized size = 0. \[ \int \frac{\left (1+b x^4\right )^p}{\left (1-x^2\right )^3} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(1 + b*x^4)^p/(1 - x^2)^3,x]
[Out]
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Maple [F] time = 0.107, size = 0, normalized size = 0. \[ \int{\frac{ \left ( b{x}^{4}+1 \right ) ^{p}}{ \left ( -{x}^{2}+1 \right ) ^{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^4+1)^p/(-x^2+1)^3,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ -\int \frac{{\left (b x^{4} + 1\right )}^{p}}{{\left (x^{2} - 1\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x^4 + 1)^p/(x^2 - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (-\frac{{\left (b x^{4} + 1\right )}^{p}}{x^{6} - 3 \, x^{4} + 3 \, x^{2} - 1}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x^4 + 1)^p/(x^2 - 1)^3,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+1)**p/(-x**2+1)**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int -\frac{{\left (b x^{4} + 1\right )}^{p}}{{\left (x^{2} - 1\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x^4 + 1)^p/(x^2 - 1)^3,x, algorithm="giac")
[Out]