Optimal. Leaf size=60 \[ a^2 d x+\frac{1}{3} a^2 e x^3+\frac{2}{5} a c d x^5+\frac{2}{7} a c e x^7+\frac{1}{9} c^2 d x^9+\frac{1}{11} c^2 e x^{11} \]
[Out]
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Rubi [A] time = 0.0646378, antiderivative size = 60, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ a^2 d x+\frac{1}{3} a^2 e x^3+\frac{2}{5} a c d x^5+\frac{2}{7} a c e x^7+\frac{1}{9} c^2 d x^9+\frac{1}{11} c^2 e x^{11} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x^2)*(a + c*x^4)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{2} e x^{3}}{3} + a^{2} \int d\, dx + \frac{2 a c d x^{5}}{5} + \frac{2 a c e x^{7}}{7} + \frac{c^{2} d x^{9}}{9} + \frac{c^{2} e x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x**2+d)*(c*x**4+a)**2,x)
[Out]
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Mathematica [A] time = 0.00456328, size = 60, normalized size = 1. \[ a^2 d x+\frac{1}{3} a^2 e x^3+\frac{2}{5} a c d x^5+\frac{2}{7} a c e x^7+\frac{1}{9} c^2 d x^9+\frac{1}{11} c^2 e x^{11} \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x^2)*(a + c*x^4)^2,x]
[Out]
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Maple [A] time = 0.001, size = 51, normalized size = 0.9 \[{a}^{2}dx+{\frac{{a}^{2}e{x}^{3}}{3}}+{\frac{2\,acd{x}^{5}}{5}}+{\frac{2\,ace{x}^{7}}{7}}+{\frac{{c}^{2}d{x}^{9}}{9}}+{\frac{{c}^{2}e{x}^{11}}{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x^2+d)*(c*x^4+a)^2,x)
[Out]
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Maxima [A] time = 0.732181, size = 68, normalized size = 1.13 \[ \frac{1}{11} \, c^{2} e x^{11} + \frac{1}{9} \, c^{2} d x^{9} + \frac{2}{7} \, a c e x^{7} + \frac{2}{5} \, a c d x^{5} + \frac{1}{3} \, a^{2} e x^{3} + a^{2} d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2*(e*x^2 + d),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.256993, size = 1, normalized size = 0.02 \[ \frac{1}{11} x^{11} e c^{2} + \frac{1}{9} x^{9} d c^{2} + \frac{2}{7} x^{7} e c a + \frac{2}{5} x^{5} d c a + \frac{1}{3} x^{3} e a^{2} + x d a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2*(e*x^2 + d),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.108154, size = 60, normalized size = 1. \[ a^{2} d x + \frac{a^{2} e x^{3}}{3} + \frac{2 a c d x^{5}}{5} + \frac{2 a c e x^{7}}{7} + \frac{c^{2} d x^{9}}{9} + \frac{c^{2} e x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x**2+d)*(c*x**4+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.268951, size = 72, normalized size = 1.2 \[ \frac{1}{11} \, c^{2} x^{11} e + \frac{1}{9} \, c^{2} d x^{9} + \frac{2}{7} \, a c x^{7} e + \frac{2}{5} \, a c d x^{5} + \frac{1}{3} \, a^{2} x^{3} e + a^{2} d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2*(e*x^2 + d),x, algorithm="giac")
[Out]