Optimal. Leaf size=54 \[ \frac{a^2 x^3}{3}+\frac{1}{7} x^7 \left (2 a c+b^2\right )+\frac{2}{5} a b x^5+\frac{2}{9} b c x^9+\frac{c^2 x^{11}}{11} \]
[Out]
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Rubi [A] time = 0.0615135, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{a^2 x^3}{3}+\frac{1}{7} x^7 \left (2 a c+b^2\right )+\frac{2}{5} a b x^5+\frac{2}{9} b c x^9+\frac{c^2 x^{11}}{11} \]
Antiderivative was successfully verified.
[In] Int[(a*x + b*x^3 + c*x^5)^2,x]
[Out]
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Rubi in Sympy [A] time = 13.772, size = 51, normalized size = 0.94 \[ \frac{a^{2} x^{3}}{3} + \frac{2 a b x^{5}}{5} + \frac{2 b c x^{9}}{9} + \frac{c^{2} x^{11}}{11} + x^{7} \left (\frac{2 a c}{7} + \frac{b^{2}}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**5+b*x**3+a*x)**2,x)
[Out]
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Mathematica [A] time = 0.00967181, size = 54, normalized size = 1. \[ \frac{a^2 x^3}{3}+\frac{1}{7} x^7 \left (2 a c+b^2\right )+\frac{2}{5} a b x^5+\frac{2}{9} b c x^9+\frac{c^2 x^{11}}{11} \]
Antiderivative was successfully verified.
[In] Integrate[(a*x + b*x^3 + c*x^5)^2,x]
[Out]
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Maple [A] time = 0.002, size = 45, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{3}}{3}}+{\frac{2\,ab{x}^{5}}{5}}+{\frac{ \left ( 2\,ac+{b}^{2} \right ){x}^{7}}{7}}+{\frac{2\,bc{x}^{9}}{9}}+{\frac{{c}^{2}{x}^{11}}{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^5+b*x^3+a*x)^2,x)
[Out]
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Maxima [A] time = 0.769016, size = 65, normalized size = 1.2 \[ \frac{1}{11} \, c^{2} x^{11} + \frac{2}{9} \, b c x^{9} + \frac{1}{7} \, b^{2} x^{7} + \frac{1}{3} \, a^{2} x^{3} + \frac{2}{35} \,{\left (5 \, c x^{7} + 7 \, b x^{5}\right )} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^5 + b*x^3 + a*x)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247831, size = 1, normalized size = 0.02 \[ \frac{1}{11} x^{11} c^{2} + \frac{2}{9} x^{9} c b + \frac{1}{7} x^{7} b^{2} + \frac{2}{7} x^{7} c a + \frac{2}{5} x^{5} b a + \frac{1}{3} x^{3} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^5 + b*x^3 + a*x)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.103182, size = 51, normalized size = 0.94 \[ \frac{a^{2} x^{3}}{3} + \frac{2 a b x^{5}}{5} + \frac{2 b c x^{9}}{9} + \frac{c^{2} x^{11}}{11} + x^{7} \left (\frac{2 a c}{7} + \frac{b^{2}}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**5+b*x**3+a*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.276552, size = 62, normalized size = 1.15 \[ \frac{1}{11} \, c^{2} x^{11} + \frac{2}{9} \, b c x^{9} + \frac{1}{7} \, b^{2} x^{7} + \frac{2}{7} \, a c x^{7} + \frac{2}{5} \, a b x^{5} + \frac{1}{3} \, a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^5 + b*x^3 + a*x)^2,x, algorithm="giac")
[Out]