Optimal. Leaf size=25 \[ c d^2 x+c d e x^2+\frac{1}{3} c e^2 x^3 \]
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Rubi [A] time = 0.0205311, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ c d^2 x+c d e x^2+\frac{1}{3} c e^2 x^3 \]
Antiderivative was successfully verified.
[In] Int[c*d^2 + 2*c*d*e*x + c*e^2*x^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 2 c d e \int x\, dx + \frac{c e^{2} x^{3}}{3} + d^{2} \int c\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(c*e**2*x**2+2*c*d*e*x+c*d**2,x)
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Mathematica [A] time = 0.000104314, size = 25, normalized size = 1. \[ c d^2 x+c d e x^2+\frac{1}{3} c e^2 x^3 \]
Antiderivative was successfully verified.
[In] Integrate[c*d^2 + 2*c*d*e*x + c*e^2*x^2,x]
[Out]
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Maple [A] time = 0.001, size = 24, normalized size = 1. \[ c{d}^{2}x+cde{x}^{2}+{\frac{c{e}^{2}{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(c*e^2*x^2+2*c*d*e*x+c*d^2,x)
[Out]
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Maxima [A] time = 0.693539, size = 31, normalized size = 1.24 \[ \frac{1}{3} \, c e^{2} x^{3} + c d e x^{2} + c d^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*e^2*x^2 + 2*c*d*e*x + c*d^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.190513, size = 1, normalized size = 0.04 \[ \frac{1}{3} x^{3} e^{2} c + x^{2} e d c + x d^{2} c \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*e^2*x^2 + 2*c*d*e*x + c*d^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.08629, size = 24, normalized size = 0.96 \[ c d^{2} x + c d e x^{2} + \frac{c e^{2} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*e**2*x**2+2*c*d*e*x+c*d**2,x)
[Out]
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GIAC/XCAS [A] time = 0.207702, size = 31, normalized size = 1.24 \[ \frac{1}{3} \, c x^{3} e^{2} + c d x^{2} e + c d^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*e^2*x^2 + 2*c*d*e*x + c*d^2,x, algorithm="giac")
[Out]