Optimal. Leaf size=97 \[ \frac{1}{7} x^7 (a f+b c)+\frac{1}{8} x^8 (a g+b d)+\frac{1}{9} x^9 (a h+b e)+\frac{1}{4} a c x^4+\frac{1}{5} a d x^5+\frac{1}{6} a e x^6+\frac{1}{10} b f x^{10}+\frac{1}{11} b g x^{11}+\frac{1}{12} b h x^{12} \]
[Out]
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Rubi [A] time = 0.208474, antiderivative size = 97, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 36, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.028 \[ \frac{1}{7} x^7 (a f+b c)+\frac{1}{8} x^8 (a g+b d)+\frac{1}{9} x^9 (a h+b e)+\frac{1}{4} a c x^4+\frac{1}{5} a d x^5+\frac{1}{6} a e x^6+\frac{1}{10} b f x^{10}+\frac{1}{11} b g x^{11}+\frac{1}{12} b h x^{12} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]
[Out]
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Rubi in Sympy [A] time = 31.5982, size = 90, normalized size = 0.93 \[ \frac{a c x^{4}}{4} + \frac{a d x^{5}}{5} + \frac{a e x^{6}}{6} + \frac{b f x^{10}}{10} + \frac{b g x^{11}}{11} + \frac{b h x^{12}}{12} + x^{9} \left (\frac{a h}{9} + \frac{b e}{9}\right ) + x^{8} \left (\frac{a g}{8} + \frac{b d}{8}\right ) + x^{7} \left (\frac{a f}{7} + \frac{b c}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)
[Out]
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Mathematica [A] time = 0.0513253, size = 97, normalized size = 1. \[ \frac{1}{7} x^7 (a f+b c)+\frac{1}{8} x^8 (a g+b d)+\frac{1}{9} x^9 (a h+b e)+\frac{1}{4} a c x^4+\frac{1}{5} a d x^5+\frac{1}{6} a e x^6+\frac{1}{10} b f x^{10}+\frac{1}{11} b g x^{11}+\frac{1}{12} b h x^{12} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]
[Out]
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Maple [A] time = 0.001, size = 80, normalized size = 0.8 \[{\frac{ac{x}^{4}}{4}}+{\frac{ad{x}^{5}}{5}}+{\frac{ae{x}^{6}}{6}}+{\frac{ \left ( af+bc \right ){x}^{7}}{7}}+{\frac{ \left ( ag+bd \right ){x}^{8}}{8}}+{\frac{ \left ( ah+be \right ){x}^{9}}{9}}+{\frac{bf{x}^{10}}{10}}+{\frac{bg{x}^{11}}{11}}+{\frac{bh{x}^{12}}{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)
[Out]
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Maxima [A] time = 1.38121, size = 107, normalized size = 1.1 \[ \frac{1}{12} \, b h x^{12} + \frac{1}{11} \, b g x^{11} + \frac{1}{10} \, b f x^{10} + \frac{1}{9} \,{\left (b e + a h\right )} x^{9} + \frac{1}{8} \,{\left (b d + a g\right )} x^{8} + \frac{1}{6} \, a e x^{6} + \frac{1}{7} \,{\left (b c + a f\right )} x^{7} + \frac{1}{5} \, a d x^{5} + \frac{1}{4} \, a c x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((h*x^5 + g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213988, size = 1, normalized size = 0.01 \[ \frac{1}{12} x^{12} h b + \frac{1}{11} x^{11} g b + \frac{1}{10} x^{10} f b + \frac{1}{9} x^{9} e b + \frac{1}{9} x^{9} h a + \frac{1}{8} x^{8} d b + \frac{1}{8} x^{8} g a + \frac{1}{7} x^{7} c b + \frac{1}{7} x^{7} f a + \frac{1}{6} x^{6} e a + \frac{1}{5} x^{5} d a + \frac{1}{4} x^{4} c a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((h*x^5 + g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.068251, size = 90, normalized size = 0.93 \[ \frac{a c x^{4}}{4} + \frac{a d x^{5}}{5} + \frac{a e x^{6}}{6} + \frac{b f x^{10}}{10} + \frac{b g x^{11}}{11} + \frac{b h x^{12}}{12} + x^{9} \left (\frac{a h}{9} + \frac{b e}{9}\right ) + x^{8} \left (\frac{a g}{8} + \frac{b d}{8}\right ) + x^{7} \left (\frac{a f}{7} + \frac{b c}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)
[Out]
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GIAC/XCAS [A] time = 0.2088, size = 117, normalized size = 1.21 \[ \frac{1}{12} \, b h x^{12} + \frac{1}{11} \, b g x^{11} + \frac{1}{10} \, b f x^{10} + \frac{1}{9} \, a h x^{9} + \frac{1}{9} \, b x^{9} e + \frac{1}{8} \, b d x^{8} + \frac{1}{8} \, a g x^{8} + \frac{1}{7} \, b c x^{7} + \frac{1}{7} \, a f x^{7} + \frac{1}{6} \, a x^{6} e + \frac{1}{5} \, a d x^{5} + \frac{1}{4} \, a c x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((h*x^5 + g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)*x^3,x, algorithm="giac")
[Out]