Optimal. Leaf size=14 \[ a e x+\frac{1}{2} c d x^2 \]
[Out]
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Rubi [A] time = 0.0226458, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 33, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.03 \[ a e x+\frac{1}{2} c d x^2 \]
Antiderivative was successfully verified.
[In] Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ c d \int x\, dx + e \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d),x)
[Out]
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Mathematica [A] time = 0.00173879, size = 14, normalized size = 1. \[ a e x+\frac{1}{2} c d x^2 \]
Antiderivative was successfully verified.
[In] Integrate[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x),x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \[ aex+{\frac{cd{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a*e*d+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d),x)
[Out]
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Maxima [A] time = 0.713776, size = 16, normalized size = 1.14 \[ \frac{1}{2} \, c d x^{2} + a e x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(e*x + d),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201508, size = 16, normalized size = 1.14 \[ \frac{1}{2} \, c d x^{2} + a e x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(e*x + d),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.114115, size = 12, normalized size = 0.86 \[ a e x + \frac{c d x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d),x)
[Out]
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GIAC/XCAS [A] time = 0.210859, size = 26, normalized size = 1.86 \[ \frac{1}{2} \,{\left (c d x^{2} e^{2} + 2 \, a x e^{3}\right )} e^{\left (-2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(e*x + d),x, algorithm="giac")
[Out]