Optimal. Leaf size=34 \[ \frac{1}{2} x^2 \left (a e^2+c d^2\right )+a d e x+\frac{1}{3} c d e x^3 \]
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Rubi [A] time = 0.0306304, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{1}{2} x^2 \left (a e^2+c d^2\right )+a d e x+\frac{1}{3} c d e x^3 \]
Antiderivative was successfully verified.
[In] Int[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{c d e x^{3}}{3} + d e \int a\, dx + \left (a e^{2} + c d^{2}\right ) \int x\, dx \]
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,x)
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Mathematica [A] time = 0.0000969548, size = 38, normalized size = 1.12 \[ a d e x+\frac{1}{2} a e^2 x^2+\frac{1}{2} c d^2 x^2+\frac{1}{3} c d e x^3 \]
Antiderivative was successfully verified.
[In] Integrate[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2,x]
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Maple [A] time = 0.001, size = 31, normalized size = 0.9 \[ adex+{\frac{ \left ( a{e}^{2}+c{d}^{2} \right ){x}^{2}}{2}}+{\frac{cde{x}^{3}}{3}} \]
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,x)
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Maxima [A] time = 0.713499, size = 41, normalized size = 1.21 \[ \frac{1}{3} \, c d e x^{3} + a d e x + \frac{1}{2} \,{\left (c d^{2} + a e^{2}\right )} x^{2} \]
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,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.18286, size = 1, normalized size = 0.03 \[ \frac{1}{3} x^{3} e d c + \frac{1}{2} x^{2} d^{2} c + \frac{1}{2} x^{2} e^{2} a + x e d a \]
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,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.090911, size = 32, normalized size = 0.94 \[ a d e x + \frac{c d e x^{3}}{3} + x^{2} \left (\frac{a e^{2}}{2} + \frac{c d^{2}}{2}\right ) \]
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,x)
[Out]
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GIAC/XCAS [A] time = 0.209742, size = 42, normalized size = 1.24 \[ \frac{1}{3} \, c d x^{3} e + a d x e + \frac{1}{2} \,{\left (c d^{2} + a e^{2}\right )} x^{2} \]
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,x, algorithm="giac")
[Out]