Optimal. Leaf size=163 \[ \frac{1}{4} a^2 c x^4+\frac{1}{5} a^2 d x^5+\frac{1}{6} a^2 e x^6+\frac{1}{10} b x^{10} (2 a f+b c)+\frac{1}{7} a x^7 (a f+2 b c)+\frac{1}{11} b x^{11} (2 a g+b d)+\frac{1}{8} a x^8 (a g+2 b d)+\frac{1}{12} b x^{12} (2 a h+b e)+\frac{1}{9} a x^9 (a h+2 b e)+\frac{1}{13} b^2 f x^{13}+\frac{1}{14} b^2 g x^{14}+\frac{1}{15} b^2 h x^{15} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.388546, antiderivative size = 163, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 38, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.026 \[ \frac{1}{4} a^2 c x^4+\frac{1}{5} a^2 d x^5+\frac{1}{6} a^2 e x^6+\frac{1}{10} b x^{10} (2 a f+b c)+\frac{1}{7} a x^7 (a f+2 b c)+\frac{1}{11} b x^{11} (2 a g+b d)+\frac{1}{8} a x^8 (a g+2 b d)+\frac{1}{12} b x^{12} (2 a h+b e)+\frac{1}{9} a x^9 (a h+2 b e)+\frac{1}{13} b^2 f x^{13}+\frac{1}{14} b^2 g x^{14}+\frac{1}{15} b^2 h x^{15} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 48.5906, size = 151, normalized size = 0.93 \[ \frac{a^{2} c x^{4}}{4} + \frac{a^{2} d x^{5}}{5} + \frac{a^{2} e x^{6}}{6} + \frac{a x^{9} \left (a h + 2 b e\right )}{9} + \frac{a x^{8} \left (a g + 2 b d\right )}{8} + \frac{a x^{7} \left (a f + 2 b c\right )}{7} + \frac{b^{2} f x^{13}}{13} + \frac{b^{2} g x^{14}}{14} + \frac{b^{2} h x^{15}}{15} + \frac{b x^{12} \left (2 a h + b e\right )}{12} + \frac{b x^{11} \left (2 a g + b d\right )}{11} + \frac{b x^{10} \left (2 a f + b c\right )}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0743391, size = 163, normalized size = 1. \[ \frac{1}{4} a^2 c x^4+\frac{1}{5} a^2 d x^5+\frac{1}{6} a^2 e x^6+\frac{1}{10} b x^{10} (2 a f+b c)+\frac{1}{7} a x^7 (a f+2 b c)+\frac{1}{11} b x^{11} (2 a g+b d)+\frac{1}{8} a x^8 (a g+2 b d)+\frac{1}{12} b x^{12} (2 a h+b e)+\frac{1}{9} a x^9 (a h+2 b e)+\frac{1}{13} b^2 f x^{13}+\frac{1}{14} b^2 g x^{14}+\frac{1}{15} b^2 h x^{15} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 152, normalized size = 0.9 \[{\frac{{b}^{2}h{x}^{15}}{15}}+{\frac{{b}^{2}g{x}^{14}}{14}}+{\frac{{b}^{2}f{x}^{13}}{13}}+{\frac{ \left ( 2\,abh+{b}^{2}e \right ){x}^{12}}{12}}+{\frac{ \left ( 2\,abg+{b}^{2}d \right ){x}^{11}}{11}}+{\frac{ \left ( 2\,abf+{b}^{2}c \right ){x}^{10}}{10}}+{\frac{ \left ({a}^{2}h+2\,bea \right ){x}^{9}}{9}}+{\frac{ \left ({a}^{2}g+2\,bda \right ){x}^{8}}{8}}+{\frac{ \left ({a}^{2}f+2\,abc \right ){x}^{7}}{7}}+{\frac{{a}^{2}e{x}^{6}}{6}}+{\frac{{a}^{2}d{x}^{5}}{5}}+{\frac{{a}^{2}c{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41455, size = 204, normalized size = 1.25 \[ \frac{1}{15} \, b^{2} h x^{15} + \frac{1}{14} \, b^{2} g x^{14} + \frac{1}{13} \, b^{2} f x^{13} + \frac{1}{12} \,{\left (b^{2} e + 2 \, a b h\right )} x^{12} + \frac{1}{11} \,{\left (b^{2} d + 2 \, a b g\right )} x^{11} + \frac{1}{10} \,{\left (b^{2} c + 2 \, a b f\right )} x^{10} + \frac{1}{9} \,{\left (2 \, a b e + a^{2} h\right )} x^{9} + \frac{1}{6} \, a^{2} e x^{6} + \frac{1}{8} \,{\left (2 \, a b d + a^{2} g\right )} x^{8} + \frac{1}{5} \, a^{2} d x^{5} + \frac{1}{7} \,{\left (2 \, a b c + a^{2} f\right )} x^{7} + \frac{1}{4} \, a^{2} c x^{4} \]
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)^2*x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.213034, size = 1, normalized size = 0.01 \[ \frac{1}{15} x^{15} h b^{2} + \frac{1}{14} x^{14} g b^{2} + \frac{1}{13} x^{13} f b^{2} + \frac{1}{12} x^{12} e b^{2} + \frac{1}{6} x^{12} h b a + \frac{1}{11} x^{11} d b^{2} + \frac{2}{11} x^{11} g b a + \frac{1}{10} x^{10} c b^{2} + \frac{1}{5} x^{10} f b a + \frac{2}{9} x^{9} e b a + \frac{1}{9} x^{9} h a^{2} + \frac{1}{4} x^{8} d b a + \frac{1}{8} x^{8} g a^{2} + \frac{2}{7} x^{7} c b a + \frac{1}{7} x^{7} f a^{2} + \frac{1}{6} x^{6} e a^{2} + \frac{1}{5} x^{5} d a^{2} + \frac{1}{4} x^{4} c a^{2} \]
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)^2*x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.094831, size = 167, normalized size = 1.02 \[ \frac{a^{2} c x^{4}}{4} + \frac{a^{2} d x^{5}}{5} + \frac{a^{2} e x^{6}}{6} + \frac{b^{2} f x^{13}}{13} + \frac{b^{2} g x^{14}}{14} + \frac{b^{2} h x^{15}}{15} + x^{12} \left (\frac{a b h}{6} + \frac{b^{2} e}{12}\right ) + x^{11} \left (\frac{2 a b g}{11} + \frac{b^{2} d}{11}\right ) + x^{10} \left (\frac{a b f}{5} + \frac{b^{2} c}{10}\right ) + x^{9} \left (\frac{a^{2} h}{9} + \frac{2 a b e}{9}\right ) + x^{8} \left (\frac{a^{2} g}{8} + \frac{a b d}{4}\right ) + x^{7} \left (\frac{a^{2} f}{7} + \frac{2 a b c}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.208828, size = 216, normalized size = 1.33 \[ \frac{1}{15} \, b^{2} h x^{15} + \frac{1}{14} \, b^{2} g x^{14} + \frac{1}{13} \, b^{2} f x^{13} + \frac{1}{6} \, a b h x^{12} + \frac{1}{12} \, b^{2} x^{12} e + \frac{1}{11} \, b^{2} d x^{11} + \frac{2}{11} \, a b g x^{11} + \frac{1}{10} \, b^{2} c x^{10} + \frac{1}{5} \, a b f x^{10} + \frac{1}{9} \, a^{2} h x^{9} + \frac{2}{9} \, a b x^{9} e + \frac{1}{4} \, a b d x^{8} + \frac{1}{8} \, a^{2} g x^{8} + \frac{2}{7} \, a b c x^{7} + \frac{1}{7} \, a^{2} f x^{7} + \frac{1}{6} \, a^{2} x^{6} e + \frac{1}{5} \, a^{2} d x^{5} + \frac{1}{4} \, a^{2} c x^{4} \]
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)^2*x^3,x, algorithm="giac")
[Out]