Optimal. Leaf size=223 \[ \frac{1}{4} a^3 c x^4+\frac{1}{5} a^3 d x^5+\frac{1}{6} a^3 e x^6+\frac{1}{7} a^2 x^7 (a f+3 b c)+\frac{1}{8} a^2 x^8 (a g+3 b d)+\frac{1}{9} a^2 x^9 (a h+3 b e)+\frac{1}{13} b^2 x^{13} (3 a f+b c)+\frac{1}{14} b^2 x^{14} (3 a g+b d)+\frac{1}{15} b^2 x^{15} (3 a h+b e)+\frac{3}{10} a b x^{10} (a f+b c)+\frac{3}{11} a b x^{11} (a g+b d)+\frac{1}{4} a b x^{12} (a h+b e)+\frac{1}{16} b^3 f x^{16}+\frac{1}{17} b^3 g x^{17}+\frac{1}{18} b^3 h x^{18} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.584532, antiderivative size = 223, 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 \[ \frac{1}{4} a^3 c x^4+\frac{1}{5} a^3 d x^5+\frac{1}{6} a^3 e x^6+\frac{1}{7} a^2 x^7 (a f+3 b c)+\frac{1}{8} a^2 x^8 (a g+3 b d)+\frac{1}{9} a^2 x^9 (a h+3 b e)+\frac{1}{13} b^2 x^{13} (3 a f+b c)+\frac{1}{14} b^2 x^{14} (3 a g+b d)+\frac{1}{15} b^2 x^{15} (3 a h+b e)+\frac{3}{10} a b x^{10} (a f+b c)+\frac{3}{11} a b x^{11} (a g+b d)+\frac{1}{4} a b x^{12} (a h+b e)+\frac{1}{16} b^3 f x^{16}+\frac{1}{17} b^3 g x^{17}+\frac{1}{18} b^3 h x^{18} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 61.6473, size = 211, normalized size = 0.95 \[ \frac{a^{3} c x^{4}}{4} + \frac{a^{3} d x^{5}}{5} + \frac{a^{3} e x^{6}}{6} + \frac{a^{2} x^{9} \left (a h + 3 b e\right )}{9} + \frac{a^{2} x^{8} \left (a g + 3 b d\right )}{8} + \frac{a^{2} x^{7} \left (a f + 3 b c\right )}{7} + \frac{a b x^{12} \left (a h + b e\right )}{4} + \frac{3 a b x^{11} \left (a g + b d\right )}{11} + \frac{3 a b x^{10} \left (a f + b c\right )}{10} + \frac{b^{3} f x^{16}}{16} + \frac{b^{3} g x^{17}}{17} + \frac{b^{3} h x^{18}}{18} + \frac{b^{2} x^{15} \left (3 a h + b e\right )}{15} + \frac{b^{2} x^{14} \left (3 a g + b d\right )}{14} + \frac{b^{2} x^{13} \left (3 a f + b c\right )}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.105024, size = 223, normalized size = 1. \[ \frac{1}{4} a^3 c x^4+\frac{1}{5} a^3 d x^5+\frac{1}{6} a^3 e x^6+\frac{1}{7} a^2 x^7 (a f+3 b c)+\frac{1}{8} a^2 x^8 (a g+3 b d)+\frac{1}{9} a^2 x^9 (a h+3 b e)+\frac{1}{13} b^2 x^{13} (3 a f+b c)+\frac{1}{14} b^2 x^{14} (3 a g+b d)+\frac{1}{15} b^2 x^{15} (3 a h+b e)+\frac{3}{10} a b x^{10} (a f+b c)+\frac{3}{11} a b x^{11} (a g+b d)+\frac{1}{4} a b x^{12} (a h+b e)+\frac{1}{16} b^3 f x^{16}+\frac{1}{17} b^3 g x^{17}+\frac{1}{18} b^3 h x^{18} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0., size = 224, normalized size = 1. \[{\frac{{b}^{3}h{x}^{18}}{18}}+{\frac{{b}^{3}g{x}^{17}}{17}}+{\frac{{b}^{3}f{x}^{16}}{16}}+{\frac{ \left ( 3\,a{b}^{2}h+{b}^{3}e \right ){x}^{15}}{15}}+{\frac{ \left ( 3\,a{b}^{2}g+{b}^{3}d \right ){x}^{14}}{14}}+{\frac{ \left ( 3\,a{b}^{2}f+{b}^{3}c \right ){x}^{13}}{13}}+{\frac{ \left ( 3\,{a}^{2}bh+3\,ae{b}^{2} \right ){x}^{12}}{12}}+{\frac{ \left ( 3\,{a}^{2}bg+3\,a{b}^{2}d \right ){x}^{11}}{11}}+{\frac{ \left ( 3\,{a}^{2}bf+3\,ac{b}^{2} \right ){x}^{10}}{10}}+{\frac{ \left ({a}^{3}h+3\,{a}^{2}be \right ){x}^{9}}{9}}+{\frac{ \left ({a}^{3}g+3\,{a}^{2}bd \right ){x}^{8}}{8}}+{\frac{ \left ({a}^{3}f+3\,{a}^{2}bc \right ){x}^{7}}{7}}+{\frac{{a}^{3}e{x}^{6}}{6}}+{\frac{{a}^{3}d{x}^{5}}{5}}+{\frac{{a}^{3}c{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41636, size = 293, normalized size = 1.31 \[ \frac{1}{18} \, b^{3} h x^{18} + \frac{1}{17} \, b^{3} g x^{17} + \frac{1}{16} \, b^{3} f x^{16} + \frac{1}{15} \,{\left (b^{3} e + 3 \, a b^{2} h\right )} x^{15} + \frac{1}{14} \,{\left (b^{3} d + 3 \, a b^{2} g\right )} x^{14} + \frac{1}{13} \,{\left (b^{3} c + 3 \, a b^{2} f\right )} x^{13} + \frac{1}{4} \,{\left (a b^{2} e + a^{2} b h\right )} x^{12} + \frac{3}{11} \,{\left (a b^{2} d + a^{2} b g\right )} x^{11} + \frac{3}{10} \,{\left (a b^{2} c + a^{2} b f\right )} x^{10} + \frac{1}{6} \, a^{3} e x^{6} + \frac{1}{9} \,{\left (3 \, a^{2} b e + a^{3} h\right )} x^{9} + \frac{1}{5} \, a^{3} d x^{5} + \frac{1}{8} \,{\left (3 \, a^{2} b d + a^{3} g\right )} x^{8} + \frac{1}{4} \, a^{3} c x^{4} + \frac{1}{7} \,{\left (3 \, a^{2} b c + a^{3} f\right )} x^{7} \]
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)^3*x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.222007, size = 1, normalized size = 0. \[ \frac{1}{18} x^{18} h b^{3} + \frac{1}{17} x^{17} g b^{3} + \frac{1}{16} x^{16} f b^{3} + \frac{1}{15} x^{15} e b^{3} + \frac{1}{5} x^{15} h b^{2} a + \frac{1}{14} x^{14} d b^{3} + \frac{3}{14} x^{14} g b^{2} a + \frac{1}{13} x^{13} c b^{3} + \frac{3}{13} x^{13} f b^{2} a + \frac{1}{4} x^{12} e b^{2} a + \frac{1}{4} x^{12} h b a^{2} + \frac{3}{11} x^{11} d b^{2} a + \frac{3}{11} x^{11} g b a^{2} + \frac{3}{10} x^{10} c b^{2} a + \frac{3}{10} x^{10} f b a^{2} + \frac{1}{3} x^{9} e b a^{2} + \frac{1}{9} x^{9} h a^{3} + \frac{3}{8} x^{8} d b a^{2} + \frac{1}{8} x^{8} g a^{3} + \frac{3}{7} x^{7} c b a^{2} + \frac{1}{7} x^{7} f a^{3} + \frac{1}{6} x^{6} e a^{3} + \frac{1}{5} x^{5} d a^{3} + \frac{1}{4} x^{4} c a^{3} \]
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)^3*x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.117227, size = 246, normalized size = 1.1 \[ \frac{a^{3} c x^{4}}{4} + \frac{a^{3} d x^{5}}{5} + \frac{a^{3} e x^{6}}{6} + \frac{b^{3} f x^{16}}{16} + \frac{b^{3} g x^{17}}{17} + \frac{b^{3} h x^{18}}{18} + x^{15} \left (\frac{a b^{2} h}{5} + \frac{b^{3} e}{15}\right ) + x^{14} \left (\frac{3 a b^{2} g}{14} + \frac{b^{3} d}{14}\right ) + x^{13} \left (\frac{3 a b^{2} f}{13} + \frac{b^{3} c}{13}\right ) + x^{12} \left (\frac{a^{2} b h}{4} + \frac{a b^{2} e}{4}\right ) + x^{11} \left (\frac{3 a^{2} b g}{11} + \frac{3 a b^{2} d}{11}\right ) + x^{10} \left (\frac{3 a^{2} b f}{10} + \frac{3 a b^{2} c}{10}\right ) + x^{9} \left (\frac{a^{3} h}{9} + \frac{a^{2} b e}{3}\right ) + x^{8} \left (\frac{a^{3} g}{8} + \frac{3 a^{2} b d}{8}\right ) + x^{7} \left (\frac{a^{3} f}{7} + \frac{3 a^{2} b c}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.215923, size = 315, normalized size = 1.41 \[ \frac{1}{18} \, b^{3} h x^{18} + \frac{1}{17} \, b^{3} g x^{17} + \frac{1}{16} \, b^{3} f x^{16} + \frac{1}{5} \, a b^{2} h x^{15} + \frac{1}{15} \, b^{3} x^{15} e + \frac{1}{14} \, b^{3} d x^{14} + \frac{3}{14} \, a b^{2} g x^{14} + \frac{1}{13} \, b^{3} c x^{13} + \frac{3}{13} \, a b^{2} f x^{13} + \frac{1}{4} \, a^{2} b h x^{12} + \frac{1}{4} \, a b^{2} x^{12} e + \frac{3}{11} \, a b^{2} d x^{11} + \frac{3}{11} \, a^{2} b g x^{11} + \frac{3}{10} \, a b^{2} c x^{10} + \frac{3}{10} \, a^{2} b f x^{10} + \frac{1}{9} \, a^{3} h x^{9} + \frac{1}{3} \, a^{2} b x^{9} e + \frac{3}{8} \, a^{2} b d x^{8} + \frac{1}{8} \, a^{3} g x^{8} + \frac{3}{7} \, a^{2} b c x^{7} + \frac{1}{7} \, a^{3} f x^{7} + \frac{1}{6} \, a^{3} x^{6} e + \frac{1}{5} \, a^{3} d x^{5} + \frac{1}{4} \, a^{3} c x^{4} \]
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)^3*x^3,x, algorithm="giac")
[Out]