Optimal. Leaf size=223 \[ \frac {1}{5} a^3 c x^5+\frac {1}{6} a^3 d x^6+\frac {1}{7} a^3 e x^7+\frac {1}{8} a^2 x^8 (a f+3 b c)+\frac {1}{9} a^2 x^9 (a g+3 b d)+\frac {1}{10} a^2 x^{10} (a h+3 b e)+\frac {1}{14} b^2 x^{14} (3 a f+b c)+\frac {1}{15} b^2 x^{15} (3 a g+b d)+\frac {1}{16} b^2 x^{16} (3 a h+b e)+\frac {3}{11} a b x^{11} (a f+b c)+\frac {1}{4} a b x^{12} (a g+b d)+\frac {3}{13} a b x^{13} (a h+b e)+\frac {1}{17} b^3 f x^{17}+\frac {1}{18} b^3 g x^{18}+\frac {1}{19} b^3 h x^{19} \]
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Rubi [A] time = 0.29, antiderivative size = 223, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {1820} \[ \frac {1}{8} a^2 x^8 (a f+3 b c)+\frac {1}{9} a^2 x^9 (a g+3 b d)+\frac {1}{10} a^2 x^{10} (a h+3 b e)+\frac {1}{5} a^3 c x^5+\frac {1}{6} a^3 d x^6+\frac {1}{7} a^3 e x^7+\frac {1}{14} b^2 x^{14} (3 a f+b c)+\frac {1}{15} b^2 x^{15} (3 a g+b d)+\frac {1}{16} b^2 x^{16} (3 a h+b e)+\frac {3}{11} a b x^{11} (a f+b c)+\frac {1}{4} a b x^{12} (a g+b d)+\frac {3}{13} a b x^{13} (a h+b e)+\frac {1}{17} b^3 f x^{17}+\frac {1}{18} b^3 g x^{18}+\frac {1}{19} b^3 h x^{19} \]
Antiderivative was successfully verified.
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Rule 1820
Rubi steps
\begin {align*} \int x^4 \left (a+b x^3\right )^3 \left (c+d x+e x^2+f x^3+g x^4+h x^5\right ) \, dx &=\int \left (a^3 c x^4+a^3 d x^5+a^3 e x^6+a^2 (3 b c+a f) x^7+a^2 (3 b d+a g) x^8+a^2 (3 b e+a h) x^9+3 a b (b c+a f) x^{10}+3 a b (b d+a g) x^{11}+3 a b (b e+a h) x^{12}+b^2 (b c+3 a f) x^{13}+b^2 (b d+3 a g) x^{14}+b^2 (b e+3 a h) x^{15}+b^3 f x^{16}+b^3 g x^{17}+b^3 h x^{18}\right ) \, dx\\ &=\frac {1}{5} a^3 c x^5+\frac {1}{6} a^3 d x^6+\frac {1}{7} a^3 e x^7+\frac {1}{8} a^2 (3 b c+a f) x^8+\frac {1}{9} a^2 (3 b d+a g) x^9+\frac {1}{10} a^2 (3 b e+a h) x^{10}+\frac {3}{11} a b (b c+a f) x^{11}+\frac {1}{4} a b (b d+a g) x^{12}+\frac {3}{13} a b (b e+a h) x^{13}+\frac {1}{14} b^2 (b c+3 a f) x^{14}+\frac {1}{15} b^2 (b d+3 a g) x^{15}+\frac {1}{16} b^2 (b e+3 a h) x^{16}+\frac {1}{17} b^3 f x^{17}+\frac {1}{18} b^3 g x^{18}+\frac {1}{19} b^3 h x^{19}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 223, normalized size = 1.00 \[ \frac {1}{5} a^3 c x^5+\frac {1}{6} a^3 d x^6+\frac {1}{7} a^3 e x^7+\frac {1}{8} a^2 x^8 (a f+3 b c)+\frac {1}{9} a^2 x^9 (a g+3 b d)+\frac {1}{10} a^2 x^{10} (a h+3 b e)+\frac {1}{14} b^2 x^{14} (3 a f+b c)+\frac {1}{15} b^2 x^{15} (3 a g+b d)+\frac {1}{16} b^2 x^{16} (3 a h+b e)+\frac {3}{11} a b x^{11} (a f+b c)+\frac {1}{4} a b x^{12} (a g+b d)+\frac {3}{13} a b x^{13} (a h+b e)+\frac {1}{17} b^3 f x^{17}+\frac {1}{18} b^3 g x^{18}+\frac {1}{19} b^3 h x^{19} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 229, normalized size = 1.03 \[ \frac {1}{19} x^{19} h b^{3} + \frac {1}{18} x^{18} g b^{3} + \frac {1}{17} x^{17} f b^{3} + \frac {1}{16} x^{16} e b^{3} + \frac {3}{16} x^{16} h b^{2} a + \frac {1}{15} x^{15} d b^{3} + \frac {1}{5} x^{15} g b^{2} a + \frac {1}{14} x^{14} c b^{3} + \frac {3}{14} x^{14} f b^{2} a + \frac {3}{13} x^{13} e b^{2} a + \frac {3}{13} x^{13} h b a^{2} + \frac {1}{4} x^{12} d b^{2} a + \frac {1}{4} x^{12} g b a^{2} + \frac {3}{11} x^{11} c b^{2} a + \frac {3}{11} x^{11} f b a^{2} + \frac {3}{10} x^{10} e b a^{2} + \frac {1}{10} x^{10} h a^{3} + \frac {1}{3} x^{9} d b a^{2} + \frac {1}{9} x^{9} g a^{3} + \frac {3}{8} x^{8} c b a^{2} + \frac {1}{8} x^{8} f a^{3} + \frac {1}{7} x^{7} e a^{3} + \frac {1}{6} x^{6} d a^{3} + \frac {1}{5} x^{5} c a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 233, normalized size = 1.04 \[ \frac {1}{19} \, b^{3} h x^{19} + \frac {1}{18} \, b^{3} g x^{18} + \frac {1}{17} \, b^{3} f x^{17} + \frac {3}{16} \, a b^{2} h x^{16} + \frac {1}{16} \, b^{3} x^{16} e + \frac {1}{15} \, b^{3} d x^{15} + \frac {1}{5} \, a b^{2} g x^{15} + \frac {1}{14} \, b^{3} c x^{14} + \frac {3}{14} \, a b^{2} f x^{14} + \frac {3}{13} \, a^{2} b h x^{13} + \frac {3}{13} \, a b^{2} x^{13} e + \frac {1}{4} \, a b^{2} d x^{12} + \frac {1}{4} \, a^{2} b g x^{12} + \frac {3}{11} \, a b^{2} c x^{11} + \frac {3}{11} \, a^{2} b f x^{11} + \frac {1}{10} \, a^{3} h x^{10} + \frac {3}{10} \, a^{2} b x^{10} e + \frac {1}{3} \, a^{2} b d x^{9} + \frac {1}{9} \, a^{3} g x^{9} + \frac {3}{8} \, a^{2} b c x^{8} + \frac {1}{8} \, a^{3} f x^{8} + \frac {1}{7} \, a^{3} x^{7} e + \frac {1}{6} \, a^{3} d x^{6} + \frac {1}{5} \, a^{3} c x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 224, normalized size = 1.00 \[ \frac {b^{3} h \,x^{19}}{19}+\frac {b^{3} g \,x^{18}}{18}+\frac {b^{3} f \,x^{17}}{17}+\frac {\left (3 a \,b^{2} h +b^{3} e \right ) x^{16}}{16}+\frac {\left (3 a \,b^{2} g +b^{3} d \right ) x^{15}}{15}+\frac {\left (3 a \,b^{2} f +b^{3} c \right ) x^{14}}{14}+\frac {\left (3 a^{2} b h +3 a e \,b^{2}\right ) x^{13}}{13}+\frac {\left (3 a^{2} b g +3 a \,b^{2} d \right ) x^{12}}{12}+\frac {a^{3} e \,x^{7}}{7}+\frac {\left (3 a^{2} b f +3 a \,b^{2} c \right ) x^{11}}{11}+\frac {a^{3} d \,x^{6}}{6}+\frac {\left (a^{3} h +3 a^{2} b e \right ) x^{10}}{10}+\frac {a^{3} c \,x^{5}}{5}+\frac {\left (a^{3} g +3 a^{2} d b \right ) x^{9}}{9}+\frac {\left (a^{3} f +3 a^{2} c b \right ) x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 217, normalized size = 0.97 \[ \frac {1}{19} \, b^{3} h x^{19} + \frac {1}{18} \, b^{3} g x^{18} + \frac {1}{17} \, b^{3} f x^{17} + \frac {1}{16} \, {\left (b^{3} e + 3 \, a b^{2} h\right )} x^{16} + \frac {1}{15} \, {\left (b^{3} d + 3 \, a b^{2} g\right )} x^{15} + \frac {1}{14} \, {\left (b^{3} c + 3 \, a b^{2} f\right )} x^{14} + \frac {3}{13} \, {\left (a b^{2} e + a^{2} b h\right )} x^{13} + \frac {1}{4} \, {\left (a b^{2} d + a^{2} b g\right )} x^{12} + \frac {3}{11} \, {\left (a b^{2} c + a^{2} b f\right )} x^{11} + \frac {1}{7} \, a^{3} e x^{7} + \frac {1}{10} \, {\left (3 \, a^{2} b e + a^{3} h\right )} x^{10} + \frac {1}{6} \, a^{3} d x^{6} + \frac {1}{9} \, {\left (3 \, a^{2} b d + a^{3} g\right )} x^{9} + \frac {1}{5} \, a^{3} c x^{5} + \frac {1}{8} \, {\left (3 \, a^{2} b c + a^{3} f\right )} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.17, size = 205, normalized size = 0.92 \[ x^8\,\left (\frac {f\,a^3}{8}+\frac {3\,b\,c\,a^2}{8}\right )+x^{14}\,\left (\frac {c\,b^3}{14}+\frac {3\,a\,f\,b^2}{14}\right )+x^9\,\left (\frac {g\,a^3}{9}+\frac {b\,d\,a^2}{3}\right )+x^{15}\,\left (\frac {d\,b^3}{15}+\frac {a\,g\,b^2}{5}\right )+x^{10}\,\left (\frac {h\,a^3}{10}+\frac {3\,b\,e\,a^2}{10}\right )+x^{16}\,\left (\frac {e\,b^3}{16}+\frac {3\,a\,h\,b^2}{16}\right )+\frac {a^3\,c\,x^5}{5}+\frac {a^3\,d\,x^6}{6}+\frac {a^3\,e\,x^7}{7}+\frac {b^3\,f\,x^{17}}{17}+\frac {b^3\,g\,x^{18}}{18}+\frac {b^3\,h\,x^{19}}{19}+\frac {3\,a\,b\,x^{11}\,\left (b\,c+a\,f\right )}{11}+\frac {a\,b\,x^{12}\,\left (b\,d+a\,g\right )}{4}+\frac {3\,a\,b\,x^{13}\,\left (b\,e+a\,h\right )}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 246, normalized size = 1.10 \[ \frac {a^{3} c x^{5}}{5} + \frac {a^{3} d x^{6}}{6} + \frac {a^{3} e x^{7}}{7} + \frac {b^{3} f x^{17}}{17} + \frac {b^{3} g x^{18}}{18} + \frac {b^{3} h x^{19}}{19} + x^{16} \left (\frac {3 a b^{2} h}{16} + \frac {b^{3} e}{16}\right ) + x^{15} \left (\frac {a b^{2} g}{5} + \frac {b^{3} d}{15}\right ) + x^{14} \left (\frac {3 a b^{2} f}{14} + \frac {b^{3} c}{14}\right ) + x^{13} \left (\frac {3 a^{2} b h}{13} + \frac {3 a b^{2} e}{13}\right ) + x^{12} \left (\frac {a^{2} b g}{4} + \frac {a b^{2} d}{4}\right ) + x^{11} \left (\frac {3 a^{2} b f}{11} + \frac {3 a b^{2} c}{11}\right ) + x^{10} \left (\frac {a^{3} h}{10} + \frac {3 a^{2} b e}{10}\right ) + x^{9} \left (\frac {a^{3} g}{9} + \frac {a^{2} b d}{3}\right ) + x^{8} \left (\frac {a^{3} f}{8} + \frac {3 a^{2} b c}{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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