Optimal. Leaf size=32 \[ a d x+\frac{1}{3} a e x^3+\frac{1}{5} c d x^5+\frac{1}{7} c e x^7 \]
[Out]
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Rubi [A] time = 0.0328197, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ a d x+\frac{1}{3} a e x^3+\frac{1}{5} c d x^5+\frac{1}{7} c e x^7 \]
Antiderivative was successfully verified.
[In] Int[(d + e*x^2)*(a + c*x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a e x^{3}}{3} + \frac{c d x^{5}}{5} + \frac{c e x^{7}}{7} + d \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x**2+d)*(c*x**4+a),x)
[Out]
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Mathematica [A] time = 0.00253939, size = 32, normalized size = 1. \[ a d x+\frac{1}{3} a e x^3+\frac{1}{5} c d x^5+\frac{1}{7} c e x^7 \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x^2)*(a + c*x^4),x]
[Out]
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Maple [A] time = 0.001, size = 27, normalized size = 0.8 \[ adx+{\frac{ae{x}^{3}}{3}}+{\frac{cd{x}^{5}}{5}}+{\frac{ce{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x^2+d)*(c*x^4+a),x)
[Out]
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Maxima [A] time = 0.727102, size = 35, normalized size = 1.09 \[ \frac{1}{7} \, c e x^{7} + \frac{1}{5} \, c d x^{5} + \frac{1}{3} \, a e x^{3} + a d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)*(e*x^2 + d),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.261315, size = 1, normalized size = 0.03 \[ \frac{1}{7} x^{7} e c + \frac{1}{5} x^{5} d c + \frac{1}{3} x^{3} e a + x d a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)*(e*x^2 + d),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.074758, size = 29, normalized size = 0.91 \[ a d x + \frac{a e x^{3}}{3} + \frac{c d x^{5}}{5} + \frac{c e x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x**2+d)*(c*x**4+a),x)
[Out]
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GIAC/XCAS [A] time = 0.268922, size = 38, normalized size = 1.19 \[ \frac{1}{7} \, c x^{7} e + \frac{1}{5} \, c d x^{5} + \frac{1}{3} \, a x^{3} e + a d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)*(e*x^2 + d),x, algorithm="giac")
[Out]