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 = {859}
\begin {gather*} \frac {1}{8} x^{16} (c+d x)^8 \end {gather*}
Antiderivative was successfully verified.
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Rule 859
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] Leaf count is larger than twice the leaf count of optimal. \(98\) vs. \(2(14)=28\).
time = 0.00, size = 98, normalized size = 7.00 \begin {gather*} \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} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(88\) vs.
\(2(12)=24\).
time = 0.19, size = 89, normalized size = 6.36
method | result | size |
gosper | \(\frac {x^{16} \left (d^{8} x^{8}+8 c \,d^{7} x^{7}+28 x^{6} c^{2} d^{6}+56 c^{3} d^{5} x^{5}+70 x^{4} c^{4} d^{4}+56 c^{5} d^{3} x^{3}+28 x^{2} c^{6} d^{2}+8 c^{7} d x +c^{8}\right )}{8}\) | \(88\) |
default | \(\frac {1}{8} x^{16} c^{8}+c^{7} d \,x^{17}+\frac {7}{2} x^{18} c^{6} d^{2}+7 c^{5} d^{3} x^{19}+\frac {35}{4} x^{20} c^{4} d^{4}+7 c^{3} d^{5} x^{21}+\frac {7}{2} x^{22} c^{2} d^{6}+c \,d^{7} x^{23}+\frac {1}{8} d^{8} x^{24}\) | \(89\) |
norman | \(\frac {1}{8} x^{16} c^{8}+c^{7} d \,x^{17}+\frac {7}{2} x^{18} c^{6} d^{2}+7 c^{5} d^{3} x^{19}+\frac {35}{4} x^{20} c^{4} d^{4}+7 c^{3} d^{5} x^{21}+\frac {7}{2} x^{22} c^{2} d^{6}+c \,d^{7} x^{23}+\frac {1}{8} d^{8} x^{24}\) | \(89\) |
risch | \(\frac {1}{8} x^{16} c^{8}+c^{7} d \,x^{17}+\frac {7}{2} x^{18} c^{6} d^{2}+7 c^{5} d^{3} x^{19}+\frac {35}{4} x^{20} c^{4} d^{4}+7 c^{3} d^{5} x^{21}+\frac {7}{2} x^{22} c^{2} d^{6}+c \,d^{7} x^{23}+\frac {1}{8} d^{8} x^{24}\) | \(89\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 88 vs.
\(2 (12) = 24\).
time = 0.27, size = 88, normalized size = 6.29 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 88 vs.
\(2 (12) = 24\).
time = 0.38, size = 88, normalized size = 6.29 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 97 vs.
\(2 (10) = 20\).
time = 0.02, size = 97, normalized size = 6.93 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.77, size = 15, normalized size = 1.07 \begin {gather*} \frac {1}{8} \, {\left (d x^{3} + c x^{2}\right )}^{8} \end {gather*}
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 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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