Optimal. Leaf size=14 \[ \frac {1}{14} x^{14} (b+c x)^{14} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {74} \begin {gather*} \frac {1}{14} x^{14} (b+c x)^{14} \end {gather*}
Antiderivative was successfully verified.
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Rule 74
Rubi steps
\begin {align*} \int x^{13} (b+c x)^{13} (b+2 c x) \, dx &=\frac {1}{14} x^{14} (b+c x)^{14}\\ \end {align*}
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Mathematica [B] time = 0.01, size = 172, normalized size = 12.29 \begin {gather*} \frac {b^{14} x^{14}}{14}+b^{13} c x^{15}+\frac {13}{2} b^{12} c^2 x^{16}+26 b^{11} c^3 x^{17}+\frac {143}{2} b^{10} c^4 x^{18}+143 b^9 c^5 x^{19}+\frac {429}{2} b^8 c^6 x^{20}+\frac {1716}{7} b^7 c^7 x^{21}+\frac {429}{2} b^6 c^8 x^{22}+143 b^5 c^9 x^{23}+\frac {143}{2} b^4 c^{10} x^{24}+26 b^3 c^{11} x^{25}+\frac {13}{2} b^2 c^{12} x^{26}+b c^{13} x^{27}+\frac {c^{14} x^{28}}{14} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^{13} (b+c x)^{13} (b+2 c x) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.35, size = 154, normalized size = 11.00 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.93 \begin {gather*} \frac {1}{14} \, {\left (c x^{2} + b x\right )}^{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 155, normalized size = 11.07 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.57, size = 154, normalized size = 11.00 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.16, size = 154, normalized size = 11.00 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.12, size = 175, normalized size = 12.50 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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