Optimal. Leaf size=17 \[ \frac{(d+e x)^2}{2 c e} \]
[Out]
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Rubi [A] time = 0.0138367, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{(d+e x)^2}{2 c e} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)^3/(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. \[ \frac{e \int x\, dx}{c} + \frac{\int d\, dx}{c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)
[Out]
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Mathematica [A] time = 0.00114778, size = 16, normalized size = 0.94 \[ \frac{d x+\frac{e x^2}{2}}{c} \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)^3/(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 = 15, normalized size = 0.9 \[{\frac{1}{c} \left ({\frac{e{x}^{2}}{2}}+dx \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)
[Out]
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Maxima [A] time = 0.698572, size = 20, normalized size = 1.18 \[ \frac{e x^{2} + 2 \, d x}{2 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^3/(c*e^2*x^2 + 2*c*d*e*x + c*d^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203636, size = 20, normalized size = 1.18 \[ \frac{e x^{2} + 2 \, d x}{2 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^3/(c*e^2*x^2 + 2*c*d*e*x + c*d^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.140857, size = 12, normalized size = 0.71 \[ \frac{d x}{c} + \frac{e x^{2}}{2 c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)
[Out]
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GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: NotImplementedError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^3/(c*e^2*x^2 + 2*c*d*e*x + c*d^2),x, algorithm="giac")
[Out]