Optimal. Leaf size=15 \[ \frac{1}{14} \left (b x+c x^2\right )^{14} \]
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Rubi [A] time = 0.0181078, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {629} \[ \frac{1}{14} \left (b x+c x^2\right )^{14} \]
Antiderivative was successfully verified.
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Rule 629
Rubi steps
\begin{align*} \int (b+2 c x) \left (b x+c x^2\right )^{13} \, dx &=\frac{1}{14} \left (b x+c x^2\right )^{14}\\ \end{align*}
Mathematica [B] time = 0.0062455, size = 172, normalized size = 11.47 \[ \frac{13}{2} b^2 c^{12} x^{26}+26 b^3 c^{11} x^{25}+\frac{143}{2} b^4 c^{10} x^{24}+143 b^5 c^9 x^{23}+\frac{429}{2} b^6 c^8 x^{22}+\frac{1716}{7} b^7 c^7 x^{21}+\frac{429}{2} b^8 c^6 x^{20}+143 b^9 c^5 x^{19}+\frac{143}{2} b^{10} c^4 x^{18}+26 b^{11} c^3 x^{17}+\frac{13}{2} b^{12} c^2 x^{16}+b^{13} c x^{15}+\frac{b^{14} x^{14}}{14}+b c^{13} x^{27}+\frac{c^{14} x^{28}}{14} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 155, normalized size = 10.3 \begin{align*}{\frac{{c}^{14}{x}^{28}}{14}}+b{c}^{13}{x}^{27}+{\frac{13\,{b}^{2}{c}^{12}{x}^{26}}{2}}+26\,{b}^{3}{c}^{11}{x}^{25}+{\frac{143\,{b}^{4}{c}^{10}{x}^{24}}{2}}+143\,{b}^{5}{c}^{9}{x}^{23}+{\frac{429\,{b}^{6}{c}^{8}{x}^{22}}{2}}+{\frac{1716\,{b}^{7}{c}^{7}{x}^{21}}{7}}+{\frac{429\,{b}^{8}{c}^{6}{x}^{20}}{2}}+143\,{b}^{9}{c}^{5}{x}^{19}+{\frac{143\,{b}^{10}{c}^{4}{x}^{18}}{2}}+26\,{b}^{11}{c}^{3}{x}^{17}+{\frac{13\,{b}^{12}{c}^{2}{x}^{16}}{2}}+{b}^{13}c{x}^{15}+{\frac{{b}^{14}{x}^{14}}{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.98839, size = 18, normalized size = 1.2 \begin{align*} \frac{1}{14} \,{\left (c x^{2} + b x\right )}^{14} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.21636, size = 387, normalized size = 25.8 \begin{align*} \frac{1}{14} x^{28} c^{14} + x^{27} c^{13} b + \frac{13}{2} x^{26} c^{12} b^{2} + 26 x^{25} c^{11} b^{3} + \frac{143}{2} x^{24} c^{10} b^{4} + 143 x^{23} c^{9} b^{5} + \frac{429}{2} x^{22} c^{8} b^{6} + \frac{1716}{7} x^{21} c^{7} b^{7} + \frac{429}{2} x^{20} c^{6} b^{8} + 143 x^{19} c^{5} b^{9} + \frac{143}{2} x^{18} c^{4} b^{10} + 26 x^{17} c^{3} b^{11} + \frac{13}{2} x^{16} c^{2} b^{12} + x^{15} c b^{13} + \frac{1}{14} x^{14} b^{14} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.115511, size = 175, normalized size = 11.67 \begin{align*} \frac{b^{14} x^{14}}{14} + b^{13} c x^{15} + \frac{13 b^{12} c^{2} x^{16}}{2} + 26 b^{11} c^{3} x^{17} + \frac{143 b^{10} c^{4} x^{18}}{2} + 143 b^{9} c^{5} x^{19} + \frac{429 b^{8} c^{6} x^{20}}{2} + \frac{1716 b^{7} c^{7} x^{21}}{7} + \frac{429 b^{6} c^{8} x^{22}}{2} + 143 b^{5} c^{9} x^{23} + \frac{143 b^{4} c^{10} x^{24}}{2} + 26 b^{3} c^{11} x^{25} + \frac{13 b^{2} c^{12} x^{26}}{2} + b c^{13} x^{27} + \frac{c^{14} x^{28}}{14} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.16984, size = 208, normalized size = 13.87 \begin{align*} \frac{1}{14} \, c^{14} x^{28} + b c^{13} x^{27} + \frac{13}{2} \, b^{2} c^{12} x^{26} + 26 \, b^{3} c^{11} x^{25} + \frac{143}{2} \, b^{4} c^{10} x^{24} + 143 \, b^{5} c^{9} x^{23} + \frac{429}{2} \, b^{6} c^{8} x^{22} + \frac{1716}{7} \, b^{7} c^{7} x^{21} + \frac{429}{2} \, b^{8} c^{6} x^{20} + 143 \, b^{9} c^{5} x^{19} + \frac{143}{2} \, b^{10} c^{4} x^{18} + 26 \, b^{11} c^{3} x^{17} + \frac{13}{2} \, b^{12} c^{2} x^{16} + b^{13} c x^{15} + \frac{1}{14} \, b^{14} x^{14} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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