Optimal. Leaf size=47 \[ -\frac{a^2}{7 x^7}-\frac{2 a c+b^2}{3 x^3}-\frac{2 a b}{5 x^5}-\frac{2 b c}{x}+c^2 x \]
[Out]
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Rubi [A] time = 0.0622405, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{a^2}{7 x^7}-\frac{2 a c+b^2}{3 x^3}-\frac{2 a b}{5 x^5}-\frac{2 b c}{x}+c^2 x \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2 + c*x^4)^2/x^8,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{2}}{7 x^{7}} - \frac{2 a b}{5 x^{5}} - \frac{2 b c}{x} + \int c^{2}\, dx - \frac{\frac{2 a c}{3} + \frac{b^{2}}{3}}{x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2+a)**2/x**8,x)
[Out]
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Mathematica [A] time = 0.042591, size = 49, normalized size = 1.04 \[ -\frac{a^2}{7 x^7}+\frac{-2 a c-b^2}{3 x^3}-\frac{2 a b}{5 x^5}-\frac{2 b c}{x}+c^2 x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2 + c*x^4)^2/x^8,x]
[Out]
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Maple [A] time = 0.008, size = 42, normalized size = 0.9 \[{c}^{2}x-{\frac{2\,ac+{b}^{2}}{3\,{x}^{3}}}-2\,{\frac{bc}{x}}-{\frac{2\,ab}{5\,{x}^{5}}}-{\frac{{a}^{2}}{7\,{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2+a)^2/x^8,x)
[Out]
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Maxima [A] time = 0.691059, size = 59, normalized size = 1.26 \[ c^{2} x - \frac{210 \, b c x^{6} + 35 \,{\left (b^{2} + 2 \, a c\right )} x^{4} + 42 \, a b x^{2} + 15 \, a^{2}}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248692, size = 62, normalized size = 1.32 \[ \frac{105 \, c^{2} x^{8} - 210 \, b c x^{6} - 35 \,{\left (b^{2} + 2 \, a c\right )} x^{4} - 42 \, a b x^{2} - 15 \, a^{2}}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.89466, size = 44, normalized size = 0.94 \[ c^{2} x - \frac{15 a^{2} + 42 a b x^{2} + 210 b c x^{6} + x^{4} \left (70 a c + 35 b^{2}\right )}{105 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2+a)**2/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.261715, size = 62, normalized size = 1.32 \[ c^{2} x - \frac{210 \, b c x^{6} + 35 \, b^{2} x^{4} + 70 \, a c x^{4} + 42 \, a b x^{2} + 15 \, a^{2}}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^8,x, algorithm="giac")
[Out]