Optimal. Leaf size=18 \[ -\frac{1}{14 \left (a+b x^2+c x^4\right )^7} \]
[Out]
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Rubi [A] time = 0.0120266, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ -\frac{1}{14 \left (a+b x^2+c x^4\right )^7} \]
Antiderivative was successfully verified.
[In] Int[(x*(b + 2*c*x^2))/(a + b*x^2 + c*x^4)^8,x]
[Out]
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Rubi in Sympy [A] time = 4.9566, size = 17, normalized size = 0.94 \[ - \frac{1}{14 \left (a + b x^{2} + c x^{4}\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(2*c*x**2+b)/(c*x**4+b*x**2+a)**8,x)
[Out]
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Mathematica [A] time = 0.0204354, size = 18, normalized size = 1. \[ -\frac{1}{14 \left (a+b x^2+c x^4\right )^7} \]
Antiderivative was successfully verified.
[In] Integrate[(x*(b + 2*c*x^2))/(a + b*x^2 + c*x^4)^8,x]
[Out]
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Maple [A] time = 0.002, size = 17, normalized size = 0.9 \[ -{\frac{1}{14\, \left ( c{x}^{4}+b{x}^{2}+a \right ) ^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(2*c*x^2+b)/(c*x^4+b*x^2+a)^8,x)
[Out]
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Maxima [A] time = 0.858208, size = 475, normalized size = 26.39 \[ -\frac{1}{14 \,{\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 7 \,{\left (3 \, b^{2} c^{5} + a c^{6}\right )} x^{24} + 7 \,{\left (5 \, b^{3} c^{4} + 6 \, a b c^{5}\right )} x^{22} + 7 \,{\left (5 \, b^{4} c^{3} + 15 \, a b^{2} c^{4} + 3 \, a^{2} c^{5}\right )} x^{20} + 7 \,{\left (3 \, b^{5} c^{2} + 20 \, a b^{3} c^{3} + 15 \, a^{2} b c^{4}\right )} x^{18} + 7 \,{\left (b^{6} c + 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} + 5 \, a^{3} c^{4}\right )} x^{16} +{\left (b^{7} + 42 \, a b^{5} c + 210 \, a^{2} b^{3} c^{2} + 140 \, a^{3} b c^{3}\right )} x^{14} + 7 \,{\left (a b^{6} + 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} + 5 \, a^{4} c^{3}\right )} x^{12} + 7 \,{\left (3 \, a^{2} b^{5} + 20 \, a^{3} b^{3} c + 15 \, a^{4} b c^{2}\right )} x^{10} + 7 \, a^{6} b x^{2} + 7 \,{\left (5 \, a^{3} b^{4} + 15 \, a^{4} b^{2} c + 3 \, a^{5} c^{2}\right )} x^{8} + a^{7} + 7 \,{\left (5 \, a^{4} b^{3} + 6 \, a^{5} b c\right )} x^{6} + 7 \,{\left (3 \, a^{5} b^{2} + a^{6} c\right )} x^{4}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^2 + b)*x/(c*x^4 + b*x^2 + a)^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.371777, size = 475, normalized size = 26.39 \[ -\frac{1}{14 \,{\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 7 \,{\left (3 \, b^{2} c^{5} + a c^{6}\right )} x^{24} + 7 \,{\left (5 \, b^{3} c^{4} + 6 \, a b c^{5}\right )} x^{22} + 7 \,{\left (5 \, b^{4} c^{3} + 15 \, a b^{2} c^{4} + 3 \, a^{2} c^{5}\right )} x^{20} + 7 \,{\left (3 \, b^{5} c^{2} + 20 \, a b^{3} c^{3} + 15 \, a^{2} b c^{4}\right )} x^{18} + 7 \,{\left (b^{6} c + 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} + 5 \, a^{3} c^{4}\right )} x^{16} +{\left (b^{7} + 42 \, a b^{5} c + 210 \, a^{2} b^{3} c^{2} + 140 \, a^{3} b c^{3}\right )} x^{14} + 7 \,{\left (a b^{6} + 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} + 5 \, a^{4} c^{3}\right )} x^{12} + 7 \,{\left (3 \, a^{2} b^{5} + 20 \, a^{3} b^{3} c + 15 \, a^{4} b c^{2}\right )} x^{10} + 7 \, a^{6} b x^{2} + 7 \,{\left (5 \, a^{3} b^{4} + 15 \, a^{4} b^{2} c + 3 \, a^{5} c^{2}\right )} x^{8} + a^{7} + 7 \,{\left (5 \, a^{4} b^{3} + 6 \, a^{5} b c\right )} x^{6} + 7 \,{\left (3 \, a^{5} b^{2} + a^{6} c\right )} x^{4}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^2 + b)*x/(c*x^4 + b*x^2 + a)^8,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(x*(2*c*x**2+b)/(c*x**4+b*x**2+a)**8,x)
[Out]
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GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^2 + b)*x/(c*x^4 + b*x^2 + a)^8,x, algorithm="giac")
[Out]