Optimal. Leaf size=97 \[ \frac{1}{5} x^5 (a f+b c)+\frac{1}{6} x^6 (a g+b d)+\frac{1}{7} x^7 (a h+b e)+\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{8} b f x^8+\frac{1}{9} b g x^9+\frac{1}{10} b h x^{10} \]
[Out]
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Rubi [A] time = 0.191875, antiderivative size = 97, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 34, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.029 \[ \frac{1}{5} x^5 (a f+b c)+\frac{1}{6} x^6 (a g+b d)+\frac{1}{7} x^7 (a h+b e)+\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{8} b f x^8+\frac{1}{9} b g x^9+\frac{1}{10} b h x^{10} \]
Antiderivative was successfully verified.
[In] Int[x*(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 [F] time = 0., size = 0, normalized size = 0. \[ a c \int x\, dx + \frac{a d x^{3}}{3} + \frac{a e x^{4}}{4} + \frac{b f x^{8}}{8} + \frac{b g x^{9}}{9} + \frac{b h x^{10}}{10} + x^{7} \left (\frac{a h}{7} + \frac{b e}{7}\right ) + x^{6} \left (\frac{a g}{6} + \frac{b d}{6}\right ) + x^{5} \left (\frac{a f}{5} + \frac{b c}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(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 = 0.037806, size = 97, normalized size = 1. \[ \frac{1}{5} x^5 (a f+b c)+\frac{1}{6} x^6 (a g+b d)+\frac{1}{7} x^7 (a h+b e)+\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{8} b f x^8+\frac{1}{9} b g x^9+\frac{1}{10} b h x^{10} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]
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Maple [A] time = 0.002, size = 80, normalized size = 0.8 \[{\frac{ac{x}^{2}}{2}}+{\frac{ad{x}^{3}}{3}}+{\frac{ae{x}^{4}}{4}}+{\frac{ \left ( af+bc \right ){x}^{5}}{5}}+{\frac{ \left ( ag+bd \right ){x}^{6}}{6}}+{\frac{ \left ( ah+be \right ){x}^{7}}{7}}+{\frac{bf{x}^{8}}{8}}+{\frac{bg{x}^{9}}{9}}+{\frac{bh{x}^{10}}{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(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 = 1.42201, size = 107, normalized size = 1.1 \[ \frac{1}{10} \, b h x^{10} + \frac{1}{9} \, b g x^{9} + \frac{1}{8} \, b f x^{8} + \frac{1}{7} \,{\left (b e + a h\right )} x^{7} + \frac{1}{6} \,{\left (b d + a g\right )} x^{6} + \frac{1}{4} \, a e x^{4} + \frac{1}{5} \,{\left (b c + a f\right )} x^{5} + \frac{1}{3} \, a d x^{3} + \frac{1}{2} \, a c x^{2} \]
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,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207261, size = 1, normalized size = 0.01 \[ \frac{1}{10} x^{10} h b + \frac{1}{9} x^{9} g b + \frac{1}{8} x^{8} f b + \frac{1}{7} x^{7} e b + \frac{1}{7} x^{7} h a + \frac{1}{6} x^{6} d b + \frac{1}{6} x^{6} g a + \frac{1}{5} x^{5} c b + \frac{1}{5} x^{5} f a + \frac{1}{4} x^{4} e a + \frac{1}{3} x^{3} d a + \frac{1}{2} x^{2} c a \]
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,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.067214, size = 90, normalized size = 0.93 \[ \frac{a c x^{2}}{2} + \frac{a d x^{3}}{3} + \frac{a e x^{4}}{4} + \frac{b f x^{8}}{8} + \frac{b g x^{9}}{9} + \frac{b h x^{10}}{10} + x^{7} \left (\frac{a h}{7} + \frac{b e}{7}\right ) + x^{6} \left (\frac{a g}{6} + \frac{b d}{6}\right ) + x^{5} \left (\frac{a f}{5} + \frac{b c}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(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 = 0.207944, size = 117, normalized size = 1.21 \[ \frac{1}{10} \, b h x^{10} + \frac{1}{9} \, b g x^{9} + \frac{1}{8} \, b f x^{8} + \frac{1}{7} \, a h x^{7} + \frac{1}{7} \, b x^{7} e + \frac{1}{6} \, b d x^{6} + \frac{1}{6} \, a g x^{6} + \frac{1}{5} \, b c x^{5} + \frac{1}{5} \, a f x^{5} + \frac{1}{4} \, a x^{4} e + \frac{1}{3} \, a d x^{3} + \frac{1}{2} \, a c x^{2} \]
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,x, algorithm="giac")
[Out]