Optimal. Leaf size=17 \[ \frac{c^2 (d+e x)^2}{2 e} \]
[Out]
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Rubi [A] time = 0.0139772, 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 \[ \frac{c^2 (d+e x)^2}{2 e} \]
Antiderivative was successfully verified.
[In] Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ c^{2} e \int x\, dx + c^{2} \int d\, dx \]
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)**2/(e*x+d)**3,x)
[Out]
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Mathematica [A] time = 0.00132441, size = 16, normalized size = 0.94 \[ c^2 \left (d x+\frac{e x^2}{2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^3,x]
[Out]
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Maple [A] time = 0.001, size = 15, normalized size = 0.9 \[{c}^{2} \left ({\frac{e{x}^{2}}{2}}+dx \right ) \]
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)^2/(e*x+d)^3,x)
[Out]
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Maxima [A] time = 0.697269, size = 22, normalized size = 1.29 \[ \frac{1}{2} \, c^{2} e x^{2} + c^{2} d x \]
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)^2/(e*x + d)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214892, size = 22, normalized size = 1.29 \[ \frac{1}{2} \, c^{2} e x^{2} + c^{2} d x \]
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)^2/(e*x + d)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.177623, size = 15, normalized size = 0.88 \[ c^{2} d x + \frac{c^{2} e x^{2}}{2} \]
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)**2/(e*x+d)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.211192, size = 31, normalized size = 1.82 \[ \frac{1}{2} \,{\left (c^{2} x^{2} e^{7} + 2 \, c^{2} d x e^{6}\right )} e^{\left (-6\right )} \]
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)^2/(e*x + d)^3,x, algorithm="giac")
[Out]