Optimal. Leaf size=14 \[ c d x+\frac{1}{2} c e x^2 \]
[Out]
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Rubi [A] time = 0.0222059, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.036 \[ c d x+\frac{1}{2} c e x^2 \]
Antiderivative was successfully verified.
[In] Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)/(d + e*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ c e \int x\, dx + d \int c\, dx \]
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)/(e*x+d),x)
[Out]
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Mathematica [A] time = 0.00130169, size = 14, normalized size = 1. \[ c \left (d x+\frac{e x^2}{2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)/(d + e*x),x]
[Out]
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Maple [A] time = 0.001, size = 13, normalized size = 0.9 \[ c \left ({\frac{e{x}^{2}}{2}}+dx \right ) \]
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)/(e*x+d),x)
[Out]
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Maxima [A] time = 0.695677, size = 16, normalized size = 1.14 \[ \frac{1}{2} \, c e x^{2} + c d x \]
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)/(e*x + d),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220595, size = 16, normalized size = 1.14 \[ \frac{1}{2} \, c e x^{2} + c d x \]
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)/(e*x + d),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.111496, size = 12, normalized size = 0.86 \[ c d x + \frac{c e x^{2}}{2} \]
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)/(e*x+d),x)
[Out]
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GIAC/XCAS [A] time = 0.209216, size = 26, normalized size = 1.86 \[ \frac{1}{2} \,{\left (c x^{2} e^{3} + 2 \, c d x e^{2}\right )} e^{\left (-2\right )} \]
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)/(e*x + d),x, algorithm="giac")
[Out]