Optimal. Leaf size=48 \[ -\frac{a^4}{2 x^2}+4 a^3 b \log (x)+3 a^2 b^2 x^2+a b^3 x^4+\frac{b^4 x^6}{6} \]
[Out]
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Rubi [A] time = 0.0916041, antiderivative size = 48, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{a^4}{2 x^2}+4 a^3 b \log (x)+3 a^2 b^2 x^2+a b^3 x^4+\frac{b^4 x^6}{6} \]
Antiderivative was successfully verified.
[In] Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{4}}{2 x^{2}} + 2 a^{3} b \log{\left (x^{2} \right )} + 3 a^{2} b^{2} x^{2} + 2 a b^{3} \int ^{x^{2}} x\, dx + \frac{b^{4} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**3,x)
[Out]
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Mathematica [A] time = 0.00769079, size = 48, normalized size = 1. \[ -\frac{a^4}{2 x^2}+4 a^3 b \log (x)+3 a^2 b^2 x^2+a b^3 x^4+\frac{b^4 x^6}{6} \]
Antiderivative was successfully verified.
[In] Integrate[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^3,x]
[Out]
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Maple [A] time = 0.008, size = 45, normalized size = 0.9 \[ -{\frac{{a}^{4}}{2\,{x}^{2}}}+3\,{a}^{2}{b}^{2}{x}^{2}+a{b}^{3}{x}^{4}+{\frac{{b}^{4}{x}^{6}}{6}}+4\,{a}^{3}b\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b^2*x^4+2*a*b*x^2+a^2)^2/x^3,x)
[Out]
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Maxima [A] time = 0.703458, size = 62, normalized size = 1.29 \[ \frac{1}{6} \, b^{4} x^{6} + a b^{3} x^{4} + 3 \, a^{2} b^{2} x^{2} + 2 \, a^{3} b \log \left (x^{2}\right ) - \frac{a^{4}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.264049, size = 66, normalized size = 1.38 \[ \frac{b^{4} x^{8} + 6 \, a b^{3} x^{6} + 18 \, a^{2} b^{2} x^{4} + 24 \, a^{3} b x^{2} \log \left (x\right ) - 3 \, a^{4}}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.15638, size = 46, normalized size = 0.96 \[ - \frac{a^{4}}{2 x^{2}} + 4 a^{3} b \log{\left (x \right )} + 3 a^{2} b^{2} x^{2} + a b^{3} x^{4} + \frac{b^{4} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.270609, size = 76, normalized size = 1.58 \[ \frac{1}{6} \, b^{4} x^{6} + a b^{3} x^{4} + 3 \, a^{2} b^{2} x^{2} + 2 \, a^{3} b{\rm ln}\left (x^{2}\right ) - \frac{4 \, a^{3} b x^{2} + a^{4}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2/x^3,x, algorithm="giac")
[Out]