Optimal. Leaf size=14 \[ \frac {1}{8} x^{16} (c+d x)^8 \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {845} \[ \frac {1}{8} x^{16} (c+d x)^8 \]
Antiderivative was successfully verified.
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Rule 845
Rubi steps
\begin {align*} \int x^{14} (c+d x)^7 \left (2 c x+3 d x^2\right ) \, dx &=\frac {1}{8} x^{16} (c+d x)^8\\ \end {align*}
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Mathematica [B] time = 0.00, size = 98, normalized size = 7.00 \[ \frac {c^8 x^{16}}{8}+c^7 d x^{17}+\frac {7}{2} c^6 d^2 x^{18}+7 c^5 d^3 x^{19}+\frac {35}{4} c^4 d^4 x^{20}+7 c^3 d^5 x^{21}+\frac {7}{2} c^2 d^6 x^{22}+c d^7 x^{23}+\frac {d^8 x^{24}}{8} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.62, size = 88, normalized size = 6.29 \[ \frac {1}{8} x^{24} d^{8} + x^{23} d^{7} c + \frac {7}{2} x^{22} d^{6} c^{2} + 7 x^{21} d^{5} c^{3} + \frac {35}{4} x^{20} d^{4} c^{4} + 7 x^{19} d^{3} c^{5} + \frac {7}{2} x^{18} d^{2} c^{6} + x^{17} d c^{7} + \frac {1}{8} x^{16} c^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 15, normalized size = 1.07 \[ \frac {1}{8} \, {\left (d x^{3} + c x^{2}\right )}^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 89, normalized size = 6.36 \[ \frac {1}{8} d^{8} x^{24}+c \,d^{7} x^{23}+\frac {7}{2} c^{2} d^{6} x^{22}+7 c^{3} d^{5} x^{21}+\frac {35}{4} c^{4} d^{4} x^{20}+7 c^{5} d^{3} x^{19}+\frac {7}{2} c^{6} d^{2} x^{18}+c^{7} d \,x^{17}+\frac {1}{8} c^{8} x^{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.66, size = 88, normalized size = 6.29 \[ \frac {1}{8} \, d^{8} x^{24} + c d^{7} x^{23} + \frac {7}{2} \, c^{2} d^{6} x^{22} + 7 \, c^{3} d^{5} x^{21} + \frac {35}{4} \, c^{4} d^{4} x^{20} + 7 \, c^{5} d^{3} x^{19} + \frac {7}{2} \, c^{6} d^{2} x^{18} + c^{7} d x^{17} + \frac {1}{8} \, c^{8} x^{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 88, normalized size = 6.29 \[ \frac {c^8\,x^{16}}{8}+c^7\,d\,x^{17}+\frac {7\,c^6\,d^2\,x^{18}}{2}+7\,c^5\,d^3\,x^{19}+\frac {35\,c^4\,d^4\,x^{20}}{4}+7\,c^3\,d^5\,x^{21}+\frac {7\,c^2\,d^6\,x^{22}}{2}+c\,d^7\,x^{23}+\frac {d^8\,x^{24}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.09, size = 97, normalized size = 6.93 \[ \frac {c^{8} x^{16}}{8} + c^{7} d x^{17} + \frac {7 c^{6} d^{2} x^{18}}{2} + 7 c^{5} d^{3} x^{19} + \frac {35 c^{4} d^{4} x^{20}}{4} + 7 c^{3} d^{5} x^{21} + \frac {7 c^{2} d^{6} x^{22}}{2} + c d^{7} x^{23} + \frac {d^{8} x^{24}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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