Optimal. Leaf size=50 \[ a^4 \log (x)+2 a^3 b x^2+\frac{3}{2} a^2 b^2 x^4+\frac{2}{3} a b^3 x^6+\frac{b^4 x^8}{8} \]
[Out]
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Rubi [A] time = 0.0819044, antiderivative size = 50, 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 \[ a^4 \log (x)+2 a^3 b x^2+\frac{3}{2} a^2 b^2 x^4+\frac{2}{3} a b^3 x^6+\frac{b^4 x^8}{8} \]
Antiderivative was successfully verified.
[In] Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{4} \log{\left (x^{2} \right )}}{2} + 2 a^{3} b x^{2} + 3 a^{2} b^{2} \int ^{x^{2}} x\, dx + \frac{2 a b^{3} x^{6}}{3} + \frac{b^{4} x^{8}}{8} \]
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,x)
[Out]
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Mathematica [A] time = 0.00748856, size = 50, normalized size = 1. \[ a^4 \log (x)+2 a^3 b x^2+\frac{3}{2} a^2 b^2 x^4+\frac{2}{3} a b^3 x^6+\frac{b^4 x^8}{8} \]
Antiderivative was successfully verified.
[In] Integrate[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x,x]
[Out]
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Maple [A] time = 0.003, size = 45, normalized size = 0.9 \[ 2\,{a}^{3}b{x}^{2}+{\frac{3\,{a}^{2}{b}^{2}{x}^{4}}{2}}+{\frac{2\,a{b}^{3}{x}^{6}}{3}}+{\frac{{b}^{4}{x}^{8}}{8}}+{a}^{4}\ln \left ( x \right ) \]
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,x)
[Out]
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Maxima [A] time = 0.707176, size = 63, normalized size = 1.26 \[ \frac{1}{8} \, b^{4} x^{8} + \frac{2}{3} \, a b^{3} x^{6} + \frac{3}{2} \, a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + \frac{1}{2} \, a^{4} \log \left (x^{2}\right ) \]
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,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.26777, size = 59, normalized size = 1.18 \[ \frac{1}{8} \, b^{4} x^{8} + \frac{2}{3} \, a b^{3} x^{6} + \frac{3}{2} \, a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4} \log \left (x\right ) \]
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,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.11365, size = 49, normalized size = 0.98 \[ a^{4} \log{\left (x \right )} + 2 a^{3} b x^{2} + \frac{3 a^{2} b^{2} x^{4}}{2} + \frac{2 a b^{3} x^{6}}{3} + \frac{b^{4} x^{8}}{8} \]
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,x)
[Out]
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GIAC/XCAS [A] time = 0.269664, size = 63, normalized size = 1.26 \[ \frac{1}{8} \, b^{4} x^{8} + \frac{2}{3} \, a b^{3} x^{6} + \frac{3}{2} \, a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + \frac{1}{2} \, a^{4}{\rm ln}\left (x^{2}\right ) \]
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,x, algorithm="giac")
[Out]