Optimal. Leaf size=16 \[ \frac{1}{42} x^{42} \left (b+c x^3\right )^{14} \]
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Rubi [A] time = 0.0497209, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.13, Rules used = {1584, 446, 74} \[ \frac{1}{42} x^{42} \left (b+c x^3\right )^{14} \]
Antiderivative was successfully verified.
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Rule 1584
Rule 446
Rule 74
Rubi steps
\begin{align*} \int x^{28} \left (b+2 c x^3\right ) \left (b x+c x^4\right )^{13} \, dx &=\int x^{41} \left (b+c x^3\right )^{13} \left (b+2 c x^3\right ) \, dx\\ &=\frac{1}{3} \operatorname{Subst}\left (\int x^{13} (b+c x)^{13} (b+2 c x) \, dx,x,x^3\right )\\ &=\frac{1}{42} x^{42} \left (b+c x^3\right )^{14}\\ \end{align*}
Mathematica [B] time = 0.0060816, size = 186, normalized size = 11.62 \[ \frac{13}{6} b^2 c^{12} x^{78}+\frac{26}{3} b^3 c^{11} x^{75}+\frac{143}{6} b^4 c^{10} x^{72}+\frac{143}{3} b^5 c^9 x^{69}+\frac{143}{2} b^6 c^8 x^{66}+\frac{572}{7} b^7 c^7 x^{63}+\frac{143}{2} b^8 c^6 x^{60}+\frac{143}{3} b^9 c^5 x^{57}+\frac{143}{6} b^{10} c^4 x^{54}+\frac{26}{3} b^{11} c^3 x^{51}+\frac{13}{6} b^{12} c^2 x^{48}+\frac{1}{3} b^{13} c x^{45}+\frac{b^{14} x^{42}}{42}+\frac{1}{3} b c^{13} x^{81}+\frac{c^{14} x^{84}}{42} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 157, normalized size = 9.8 \begin{align*}{\frac{{c}^{14}{x}^{84}}{42}}+{\frac{b{c}^{13}{x}^{81}}{3}}+{\frac{13\,{b}^{2}{c}^{12}{x}^{78}}{6}}+{\frac{26\,{b}^{3}{c}^{11}{x}^{75}}{3}}+{\frac{143\,{b}^{4}{c}^{10}{x}^{72}}{6}}+{\frac{143\,{b}^{5}{c}^{9}{x}^{69}}{3}}+{\frac{143\,{b}^{6}{c}^{8}{x}^{66}}{2}}+{\frac{572\,{b}^{7}{c}^{7}{x}^{63}}{7}}+{\frac{143\,{b}^{8}{c}^{6}{x}^{60}}{2}}+{\frac{143\,{b}^{9}{c}^{5}{x}^{57}}{3}}+{\frac{143\,{b}^{10}{c}^{4}{x}^{54}}{6}}+{\frac{26\,{b}^{11}{c}^{3}{x}^{51}}{3}}+{\frac{13\,{b}^{12}{c}^{2}{x}^{48}}{6}}+{\frac{{b}^{13}c{x}^{45}}{3}}+{\frac{{b}^{14}{x}^{42}}{42}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.0192, size = 211, normalized size = 13.19 \begin{align*} \frac{1}{42} \, c^{14} x^{84} + \frac{1}{3} \, b c^{13} x^{81} + \frac{13}{6} \, b^{2} c^{12} x^{78} + \frac{26}{3} \, b^{3} c^{11} x^{75} + \frac{143}{6} \, b^{4} c^{10} x^{72} + \frac{143}{3} \, b^{5} c^{9} x^{69} + \frac{143}{2} \, b^{6} c^{8} x^{66} + \frac{572}{7} \, b^{7} c^{7} x^{63} + \frac{143}{2} \, b^{8} c^{6} x^{60} + \frac{143}{3} \, b^{9} c^{5} x^{57} + \frac{143}{6} \, b^{10} c^{4} x^{54} + \frac{26}{3} \, b^{11} c^{3} x^{51} + \frac{13}{6} \, b^{12} c^{2} x^{48} + \frac{1}{3} \, b^{13} c x^{45} + \frac{1}{42} \, b^{14} x^{42} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.18778, size = 408, normalized size = 25.5 \begin{align*} \frac{1}{42} x^{84} c^{14} + \frac{1}{3} x^{81} c^{13} b + \frac{13}{6} x^{78} c^{12} b^{2} + \frac{26}{3} x^{75} c^{11} b^{3} + \frac{143}{6} x^{72} c^{10} b^{4} + \frac{143}{3} x^{69} c^{9} b^{5} + \frac{143}{2} x^{66} c^{8} b^{6} + \frac{572}{7} x^{63} c^{7} b^{7} + \frac{143}{2} x^{60} c^{6} b^{8} + \frac{143}{3} x^{57} c^{5} b^{9} + \frac{143}{6} x^{54} c^{4} b^{10} + \frac{26}{3} x^{51} c^{3} b^{11} + \frac{13}{6} x^{48} c^{2} b^{12} + \frac{1}{3} x^{45} c b^{13} + \frac{1}{42} x^{42} b^{14} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.125615, size = 185, normalized size = 11.56 \begin{align*} \frac{b^{14} x^{42}}{42} + \frac{b^{13} c x^{45}}{3} + \frac{13 b^{12} c^{2} x^{48}}{6} + \frac{26 b^{11} c^{3} x^{51}}{3} + \frac{143 b^{10} c^{4} x^{54}}{6} + \frac{143 b^{9} c^{5} x^{57}}{3} + \frac{143 b^{8} c^{6} x^{60}}{2} + \frac{572 b^{7} c^{7} x^{63}}{7} + \frac{143 b^{6} c^{8} x^{66}}{2} + \frac{143 b^{5} c^{9} x^{69}}{3} + \frac{143 b^{4} c^{10} x^{72}}{6} + \frac{26 b^{3} c^{11} x^{75}}{3} + \frac{13 b^{2} c^{12} x^{78}}{6} + \frac{b c^{13} x^{81}}{3} + \frac{c^{14} x^{84}}{42} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.15298, size = 211, normalized size = 13.19 \begin{align*} \frac{1}{42} \, c^{14} x^{84} + \frac{1}{3} \, b c^{13} x^{81} + \frac{13}{6} \, b^{2} c^{12} x^{78} + \frac{26}{3} \, b^{3} c^{11} x^{75} + \frac{143}{6} \, b^{4} c^{10} x^{72} + \frac{143}{3} \, b^{5} c^{9} x^{69} + \frac{143}{2} \, b^{6} c^{8} x^{66} + \frac{572}{7} \, b^{7} c^{7} x^{63} + \frac{143}{2} \, b^{8} c^{6} x^{60} + \frac{143}{3} \, b^{9} c^{5} x^{57} + \frac{143}{6} \, b^{10} c^{4} x^{54} + \frac{26}{3} \, b^{11} c^{3} x^{51} + \frac{13}{6} \, b^{12} c^{2} x^{48} + \frac{1}{3} \, b^{13} c x^{45} + \frac{1}{42} \, b^{14} x^{42} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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