Optimal. Leaf size=46 \[ a^2 x+\frac{1}{3} x^3 \left (2 a c+b^2\right )+a b x^2+\frac{1}{2} b c x^4+\frac{c^2 x^5}{5} \]
[Out]
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Rubi [A] time = 0.0553718, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ a^2 x+\frac{1}{3} x^3 \left (2 a c+b^2\right )+a b x^2+\frac{1}{2} b c x^4+\frac{c^2 x^5}{5} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x + c*x^2)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 2 a b \int x\, dx + \frac{b c x^{4}}{2} + \frac{c^{2} x^{5}}{5} + x^{3} \left (\frac{2 a c}{3} + \frac{b^{2}}{3}\right ) + \int a^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.0123411, size = 46, normalized size = 1. \[ a^2 x+\frac{1}{3} x^3 \left (2 a c+b^2\right )+a b x^2+\frac{1}{2} b c x^4+\frac{c^2 x^5}{5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x + c*x^2)^2,x]
[Out]
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Maple [A] time = 0.001, size = 41, normalized size = 0.9 \[{a}^{2}x+ab{x}^{2}+{\frac{ \left ( 2\,ac+{b}^{2} \right ){x}^{3}}{3}}+{\frac{bc{x}^{4}}{2}}+{\frac{{c}^{2}{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+b*x+a)^2,x)
[Out]
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Maxima [A] time = 0.814393, size = 61, normalized size = 1.33 \[ \frac{1}{5} \, c^{2} x^{5} + \frac{1}{2} \, b c x^{4} + \frac{1}{3} \, b^{2} x^{3} + a^{2} x + \frac{1}{3} \,{\left (2 \, c x^{3} + 3 \, b x^{2}\right )} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.181306, size = 1, normalized size = 0.02 \[ \frac{1}{5} x^{5} c^{2} + \frac{1}{2} x^{4} c b + \frac{1}{3} x^{3} b^{2} + \frac{2}{3} x^{3} c a + x^{2} b a + x a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.101438, size = 42, normalized size = 0.91 \[ a^{2} x + a b x^{2} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{5}}{5} + x^{3} \left (\frac{2 a c}{3} + \frac{b^{2}}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.202969, size = 57, normalized size = 1.24 \[ \frac{1}{5} \, c^{2} x^{5} + \frac{1}{2} \, b c x^{4} + \frac{1}{3} \, b^{2} x^{3} + \frac{2}{3} \, a c x^{3} + a b x^{2} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^2,x, algorithm="giac")
[Out]