Optimal. Leaf size=92 \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11} \]
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Rubi [A] time = 0.104594, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x + c*x^2)*(e + f*x^4)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + b e^{2} \int x\, dx + \frac{b e f x^{6}}{3} + \frac{b f^{2} x^{10}}{10} + \frac{c e^{2} x^{3}}{3} + \frac{2 c e f x^{7}}{7} + \frac{c f^{2} x^{11}}{11} + e^{2} \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+b*x+a)*(f*x**4+e)**2,x)
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Mathematica [A] time = 0.00591937, size = 92, normalized size = 1. \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x + c*x^2)*(e + f*x^4)^2,x]
[Out]
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Maple [A] time = 0., size = 77, normalized size = 0.8 \[ a{e}^{2}x+{\frac{b{e}^{2}{x}^{2}}{2}}+{\frac{c{e}^{2}{x}^{3}}{3}}+{\frac{2\,aef{x}^{5}}{5}}+{\frac{bef{x}^{6}}{3}}+{\frac{2\,cef{x}^{7}}{7}}+{\frac{a{f}^{2}{x}^{9}}{9}}+{\frac{b{f}^{2}{x}^{10}}{10}}+{\frac{c{f}^{2}{x}^{11}}{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+b*x+a)*(f*x^4+e)^2,x)
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Maxima [A] time = 1.40846, size = 103, normalized size = 1.12 \[ \frac{1}{11} \, c f^{2} x^{11} + \frac{1}{10} \, b f^{2} x^{10} + \frac{1}{9} \, a f^{2} x^{9} + \frac{2}{7} \, c e f x^{7} + \frac{1}{3} \, b e f x^{6} + \frac{2}{5} \, a e f x^{5} + \frac{1}{3} \, c e^{2} x^{3} + \frac{1}{2} \, b e^{2} x^{2} + a e^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*(c*x^2 + b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207, size = 1, normalized size = 0.01 \[ \frac{1}{11} x^{11} f^{2} c + \frac{1}{10} x^{10} f^{2} b + \frac{1}{9} x^{9} f^{2} a + \frac{2}{7} x^{7} f e c + \frac{1}{3} x^{6} f e b + \frac{2}{5} x^{5} f e a + \frac{1}{3} x^{3} e^{2} c + \frac{1}{2} x^{2} e^{2} b + x e^{2} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*(c*x^2 + b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.064328, size = 90, normalized size = 0.98 \[ a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + \frac{b e^{2} x^{2}}{2} + \frac{b e f x^{6}}{3} + \frac{b f^{2} x^{10}}{10} + \frac{c e^{2} x^{3}}{3} + \frac{2 c e f x^{7}}{7} + \frac{c f^{2} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+b*x+a)*(f*x**4+e)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.210448, size = 103, normalized size = 1.12 \[ \frac{1}{11} \, c f^{2} x^{11} + \frac{1}{10} \, b f^{2} x^{10} + \frac{1}{9} \, a f^{2} x^{9} + \frac{2}{7} \, c f x^{7} e + \frac{1}{3} \, b f x^{6} e + \frac{2}{5} \, a f x^{5} e + \frac{1}{3} \, c x^{3} e^{2} + \frac{1}{2} \, b x^{2} e^{2} + a x e^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*(c*x^2 + b*x + a),x, algorithm="giac")
[Out]