Optimal. Leaf size=42 \[ \frac{1}{2} x^2 (a e+b d)+a d x+\frac{1}{3} x^3 (b e+c d)+\frac{1}{4} c e x^4 \]
[Out]
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Rubi [A] time = 0.0759425, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{1}{2} x^2 (a e+b d)+a d x+\frac{1}{3} x^3 (b e+c d)+\frac{1}{4} c e x^4 \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)*(a + b*x + c*x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{c e x^{4}}{4} + d \int a\, dx + x^{3} \left (\frac{b e}{3} + \frac{c d}{3}\right ) + \left (a e + b d\right ) \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(c*x**2+b*x+a),x)
[Out]
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Mathematica [A] time = 0.0252163, size = 42, normalized size = 1. \[ \frac{1}{2} x^2 (a e+b d)+a d x+\frac{1}{3} x^3 (b e+c d)+\frac{1}{4} c e x^4 \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)*(a + b*x + c*x^2),x]
[Out]
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Maple [A] time = 0.001, size = 37, normalized size = 0.9 \[ adx+{\frac{ \left ( ae+bd \right ){x}^{2}}{2}}+{\frac{ \left ( be+cd \right ){x}^{3}}{3}}+{\frac{ce{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(c*x^2+b*x+a),x)
[Out]
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Maxima [A] time = 0.812731, size = 49, normalized size = 1.17 \[ \frac{1}{4} \, c e x^{4} + \frac{1}{3} \,{\left (c d + b e\right )} x^{3} + a d x + \frac{1}{2} \,{\left (b d + a e\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(e*x + d),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.181663, size = 1, normalized size = 0.02 \[ \frac{1}{4} x^{4} e c + \frac{1}{3} x^{3} d c + \frac{1}{3} x^{3} e b + \frac{1}{2} x^{2} d b + \frac{1}{2} x^{2} e a + x d a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(e*x + d),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.091038, size = 39, normalized size = 0.93 \[ a d x + \frac{c e x^{4}}{4} + x^{3} \left (\frac{b e}{3} + \frac{c d}{3}\right ) + x^{2} \left (\frac{a e}{2} + \frac{b d}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(c*x**2+b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.201956, size = 58, normalized size = 1.38 \[ \frac{1}{4} \, c x^{4} e + \frac{1}{3} \, c d x^{3} + \frac{1}{3} \, b x^{3} e + \frac{1}{2} \, b d x^{2} + \frac{1}{2} \, a x^{2} e + a d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(e*x + d),x, algorithm="giac")
[Out]