Optimal. Leaf size=154 \[ a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{7} x^7 \left (2 a c f+b^2 f+2 b c d\right )+\frac{1}{5} x^5 \left (2 a b f+2 a c d+b^2 d\right )+\frac{1}{6} e x^6 \left (2 a c+b^2\right )+\frac{1}{3} a x^3 (a f+2 b d)+\frac{1}{2} a b e x^4+\frac{1}{9} c x^9 (2 b f+c d)+\frac{1}{4} b c e x^8+\frac{1}{10} c^2 e x^{10}+\frac{1}{11} c^2 f x^{11} \]
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Rubi [A] time = 0.334447, antiderivative size = 154, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 61, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.016 \[ a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{7} x^7 \left (2 a c f+b^2 f+2 b c d\right )+\frac{1}{5} x^5 \left (2 a b f+2 a c d+b^2 d\right )+\frac{1}{6} e x^6 \left (2 a c+b^2\right )+\frac{1}{3} a x^3 (a f+2 b d)+\frac{1}{2} a b e x^4+\frac{1}{9} c x^9 (2 b f+c d)+\frac{1}{4} b c e x^8+\frac{1}{10} c^2 e x^{10}+\frac{1}{11} c^2 f x^{11} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2 + c*x^4)*(a*d + a*e*x + (b*d + a*f)*x^2 + b*e*x^3 + (c*d + b*f)*x^4 + c*e*x^5 + c*f*x^6),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{2} e \int x\, dx + a^{2} \int d\, dx + \frac{a b e x^{4}}{2} + \frac{a x^{3} \left (a f + 2 b d\right )}{3} + \frac{b c e x^{8}}{4} + \frac{c^{2} e x^{10}}{10} + \frac{c^{2} f x^{11}}{11} + \frac{c x^{9} \left (2 b f + c d\right )}{9} + \frac{e x^{6} \left (2 a c + b^{2}\right )}{6} + x^{7} \left (\frac{2 a c f}{7} + \frac{b^{2} f}{7} + \frac{2 b c d}{7}\right ) + x^{5} \left (\frac{2 a b f}{5} + \frac{2 a c d}{5} + \frac{b^{2} d}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2+a)*(a*d+a*e*x+(a*f+b*d)*x**2+b*e*x**3+(b*f+c*d)*x**4+c*e*x**5+c*f*x**6),x)
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Mathematica [A] time = 0.0947735, size = 154, normalized size = 1. \[ a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{7} x^7 \left (2 a c f+b^2 f+2 b c d\right )+\frac{1}{5} x^5 \left (2 a b f+2 a c d+b^2 d\right )+\frac{1}{6} e x^6 \left (2 a c+b^2\right )+\frac{1}{3} a x^3 (a f+2 b d)+\frac{1}{2} a b e x^4+\frac{1}{9} c x^9 (2 b f+c d)+\frac{1}{4} b c e x^8+\frac{1}{10} c^2 e x^{10}+\frac{1}{11} c^2 f x^{11} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2 + c*x^4)*(a*d + a*e*x + (b*d + a*f)*x^2 + b*e*x^3 + (c*d + b*f)*x^4 + c*e*x^5 + c*f*x^6),x]
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Maple [A] time = 0.002, size = 161, normalized size = 1.1 \[{\frac{{c}^{2}f{x}^{11}}{11}}+{\frac{{c}^{2}e{x}^{10}}{10}}+{\frac{ \left ( bcf+c \left ( bf+cd \right ) \right ){x}^{9}}{9}}+{\frac{bce{x}^{8}}{4}}+{\frac{ \left ( acf+b \left ( bf+cd \right ) +c \left ( fa+bd \right ) \right ){x}^{7}}{7}}+{\frac{ \left ( 2\,ace+{b}^{2}e \right ){x}^{6}}{6}}+{\frac{ \left ( a \left ( bf+cd \right ) +b \left ( fa+bd \right ) +acd \right ){x}^{5}}{5}}+{\frac{abe{x}^{4}}{2}}+{\frac{ \left ( a \left ( fa+bd \right ) +abd \right ){x}^{3}}{3}}+{\frac{{a}^{2}e{x}^{2}}{2}}+{a}^{2}dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2+a)*(a*d+a*e*x+(a*f+b*d)*x^2+b*e*x^3+(b*f+c*d)*x^4+c*e*x^5+c*f*x^6),x)
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Maxima [A] time = 0.704284, size = 186, normalized size = 1.21 \[ \frac{1}{11} \, c^{2} f x^{11} + \frac{1}{10} \, c^{2} e x^{10} + \frac{1}{4} \, b c e x^{8} + \frac{1}{9} \,{\left (c^{2} d + 2 \, b c f\right )} x^{9} + \frac{1}{6} \,{\left (b^{2} + 2 \, a c\right )} e x^{6} + \frac{1}{7} \,{\left (2 \, b c d +{\left (b^{2} + 2 \, a c\right )} f\right )} x^{7} + \frac{1}{2} \, a b e x^{4} + \frac{1}{5} \,{\left (2 \, a b f +{\left (b^{2} + 2 \, a c\right )} d\right )} x^{5} + \frac{1}{2} \, a^{2} e x^{2} + a^{2} d x + \frac{1}{3} \,{\left (2 \, a b d + a^{2} f\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*f*x^6 + c*e*x^5 + b*e*x^3 + (c*d + b*f)*x^4 + a*e*x + (b*d + a*f)*x^2 + a*d)*(c*x^4 + b*x^2 + a),x, algorithm="maxima")
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Fricas [A] time = 0.245856, size = 1, normalized size = 0.01 \[ \frac{1}{11} x^{11} f c^{2} + \frac{1}{10} x^{10} e c^{2} + \frac{1}{9} x^{9} d c^{2} + \frac{2}{9} x^{9} f c b + \frac{1}{4} x^{8} e c b + \frac{2}{7} x^{7} d c b + \frac{1}{7} x^{7} f b^{2} + \frac{2}{7} x^{7} f c a + \frac{1}{6} x^{6} e b^{2} + \frac{1}{3} x^{6} e c a + \frac{1}{5} x^{5} d b^{2} + \frac{2}{5} x^{5} d c a + \frac{2}{5} x^{5} f b a + \frac{1}{2} x^{4} e b a + \frac{2}{3} x^{3} d b a + \frac{1}{3} x^{3} f a^{2} + \frac{1}{2} x^{2} e a^{2} + x d a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*f*x^6 + c*e*x^5 + b*e*x^3 + (c*d + b*f)*x^4 + a*e*x + (b*d + a*f)*x^2 + a*d)*(c*x^4 + b*x^2 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.171624, size = 165, normalized size = 1.07 \[ a^{2} d x + \frac{a^{2} e x^{2}}{2} + \frac{a b e x^{4}}{2} + \frac{b c e x^{8}}{4} + \frac{c^{2} e x^{10}}{10} + \frac{c^{2} f x^{11}}{11} + x^{9} \left (\frac{2 b c f}{9} + \frac{c^{2} d}{9}\right ) + x^{7} \left (\frac{2 a c f}{7} + \frac{b^{2} f}{7} + \frac{2 b c d}{7}\right ) + x^{6} \left (\frac{a c e}{3} + \frac{b^{2} e}{6}\right ) + x^{5} \left (\frac{2 a b f}{5} + \frac{2 a c d}{5} + \frac{b^{2} d}{5}\right ) + x^{3} \left (\frac{a^{2} f}{3} + \frac{2 a b d}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2+a)*(a*d+a*e*x+(a*f+b*d)*x**2+b*e*x**3+(b*f+c*d)*x**4+c*e*x**5+c*f*x**6),x)
[Out]
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GIAC/XCAS [A] time = 0.286999, size = 212, normalized size = 1.38 \[ \frac{1}{11} \, c^{2} f x^{11} + \frac{1}{10} \, c^{2} x^{10} e + \frac{1}{9} \, c^{2} d x^{9} + \frac{2}{9} \, b c f x^{9} + \frac{1}{4} \, b c x^{8} e + \frac{2}{7} \, b c d x^{7} + \frac{1}{7} \, b^{2} f x^{7} + \frac{2}{7} \, a c f x^{7} + \frac{1}{6} \, b^{2} x^{6} e + \frac{1}{3} \, a c x^{6} e + \frac{1}{5} \, b^{2} d x^{5} + \frac{2}{5} \, a c d x^{5} + \frac{2}{5} \, a b f x^{5} + \frac{1}{2} \, a b x^{4} e + \frac{2}{3} \, a b d x^{3} + \frac{1}{3} \, a^{2} f x^{3} + \frac{1}{2} \, a^{2} x^{2} e + a^{2} d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*f*x^6 + c*e*x^5 + b*e*x^3 + (c*d + b*f)*x^4 + a*e*x + (b*d + a*f)*x^2 + a*d)*(c*x^4 + b*x^2 + a),x, algorithm="giac")
[Out]