Optimal. Leaf size=97 \[ \frac{1}{8} x^8 (a f+b c)+\frac{1}{9} x^9 (a g+b d)+\frac{1}{10} x^{10} (a h+b e)+\frac{1}{5} a c x^5+\frac{1}{6} a d x^6+\frac{1}{7} a e x^7+\frac{1}{11} b f x^{11}+\frac{1}{12} b g x^{12}+\frac{1}{13} b h x^{13} \]
[Out]
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Rubi [A] time = 0.231481, 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 \[ \frac{1}{8} x^8 (a f+b c)+\frac{1}{9} x^9 (a g+b d)+\frac{1}{10} x^{10} (a h+b e)+\frac{1}{5} a c x^5+\frac{1}{6} a d x^6+\frac{1}{7} a e x^7+\frac{1}{11} b f x^{11}+\frac{1}{12} b g x^{12}+\frac{1}{13} b h x^{13} \]
Antiderivative was successfully verified.
[In] Int[x^4*(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 = 28.0393, size = 90, normalized size = 0.93 \[ \frac{a c x^{5}}{5} + \frac{a d x^{6}}{6} + \frac{a e x^{7}}{7} + \frac{b f x^{11}}{11} + \frac{b g x^{12}}{12} + \frac{b h x^{13}}{13} + x^{10} \left (\frac{a h}{10} + \frac{b e}{10}\right ) + x^{9} \left (\frac{a g}{9} + \frac{b d}{9}\right ) + x^{8} \left (\frac{a f}{8} + \frac{b c}{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4*(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 = 0.0513963, size = 97, normalized size = 1. \[ \frac{1}{8} x^8 (a f+b c)+\frac{1}{9} x^9 (a g+b d)+\frac{1}{10} x^{10} (a h+b e)+\frac{1}{5} a c x^5+\frac{1}{6} a d x^6+\frac{1}{7} a e x^7+\frac{1}{11} b f x^{11}+\frac{1}{12} b g x^{12}+\frac{1}{13} b h x^{13} \]
Antiderivative was successfully verified.
[In] Integrate[x^4*(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 = 0.002, size = 80, normalized size = 0.8 \[{\frac{ac{x}^{5}}{5}}+{\frac{ad{x}^{6}}{6}}+{\frac{ae{x}^{7}}{7}}+{\frac{ \left ( af+bc \right ){x}^{8}}{8}}+{\frac{ \left ( ag+bd \right ){x}^{9}}{9}}+{\frac{ \left ( ah+be \right ){x}^{10}}{10}}+{\frac{bf{x}^{11}}{11}}+{\frac{bg{x}^{12}}{12}}+{\frac{bh{x}^{13}}{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4*(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 = 1.37896, size = 107, normalized size = 1.1 \[ \frac{1}{13} \, b h x^{13} + \frac{1}{12} \, b g x^{12} + \frac{1}{11} \, b f x^{11} + \frac{1}{10} \,{\left (b e + a h\right )} x^{10} + \frac{1}{9} \,{\left (b d + a g\right )} x^{9} + \frac{1}{7} \, a e x^{7} + \frac{1}{8} \,{\left (b c + a f\right )} x^{8} + \frac{1}{6} \, a d x^{6} + \frac{1}{5} \, a c x^{5} \]
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^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229551, size = 1, normalized size = 0.01 \[ \frac{1}{13} x^{13} h b + \frac{1}{12} x^{12} g b + \frac{1}{11} x^{11} f b + \frac{1}{10} x^{10} e b + \frac{1}{10} x^{10} h a + \frac{1}{9} x^{9} d b + \frac{1}{9} x^{9} g a + \frac{1}{8} x^{8} c b + \frac{1}{8} x^{8} f a + \frac{1}{7} x^{7} e a + \frac{1}{6} x^{6} d a + \frac{1}{5} x^{5} c a \]
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^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.071243, size = 90, normalized size = 0.93 \[ \frac{a c x^{5}}{5} + \frac{a d x^{6}}{6} + \frac{a e x^{7}}{7} + \frac{b f x^{11}}{11} + \frac{b g x^{12}}{12} + \frac{b h x^{13}}{13} + x^{10} \left (\frac{a h}{10} + \frac{b e}{10}\right ) + x^{9} \left (\frac{a g}{9} + \frac{b d}{9}\right ) + x^{8} \left (\frac{a f}{8} + \frac{b c}{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4*(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 = 0.209735, size = 117, normalized size = 1.21 \[ \frac{1}{13} \, b h x^{13} + \frac{1}{12} \, b g x^{12} + \frac{1}{11} \, b f x^{11} + \frac{1}{10} \, a h x^{10} + \frac{1}{10} \, b x^{10} e + \frac{1}{9} \, b d x^{9} + \frac{1}{9} \, a g x^{9} + \frac{1}{8} \, b c x^{8} + \frac{1}{8} \, a f x^{8} + \frac{1}{7} \, a x^{7} e + \frac{1}{6} \, a d x^{6} + \frac{1}{5} \, a c x^{5} \]
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^4,x, algorithm="giac")
[Out]