Optimal. Leaf size=21 \[ \frac {x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \]
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Rubi [A]
time = 0.02, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {1598, 457, 75}
\begin {gather*} \frac {x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \end {gather*}
Antiderivative was successfully verified.
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Rule 75
Rule 457
Rule 1598
Rubi steps
\begin {align*} \int x^{14 (-1+n)} \left (b+2 c x^n\right ) \left (b x+c x^{1+n}\right )^{13} \, dx &=\int x^{13+14 (-1+n)} \left (b+c x^n\right )^{13} \left (b+2 c x^n\right ) \, dx\\ &=\frac {\text {Subst}\left (\int x^{13} (b+c x)^{13} (b+2 c x) \, dx,x,x^n\right )}{n}\\ &=\frac {x^{14 n} \left (b+c x^n\right )^{14}}{14 n}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 1.00 \begin {gather*} \frac {x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \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. \(229\) vs.
\(2(19)=38\).
time = 0.21, size = 230, normalized size = 10.95
method | result | size |
risch | \(\frac {c^{14} x^{28 n}}{14 n}+\frac {b \,c^{13} x^{27 n}}{n}+\frac {13 b^{2} c^{12} x^{26 n}}{2 n}+\frac {26 b^{3} c^{11} x^{25 n}}{n}+\frac {143 b^{4} c^{10} x^{24 n}}{2 n}+\frac {143 b^{5} c^{9} x^{23 n}}{n}+\frac {429 b^{6} c^{8} x^{22 n}}{2 n}+\frac {1716 b^{7} c^{7} x^{21 n}}{7 n}+\frac {429 b^{8} c^{6} x^{20 n}}{2 n}+\frac {143 b^{9} c^{5} x^{19 n}}{n}+\frac {143 b^{10} c^{4} x^{18 n}}{2 n}+\frac {26 b^{11} c^{3} x^{17 n}}{n}+\frac {13 b^{12} c^{2} x^{16 n}}{2 n}+\frac {b^{13} c \,x^{15 n}}{n}+\frac {b^{14} x^{14 n}}{14 n}\) | \(230\) |
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. 229 vs.
\(2 (19) = 38\).
time = 0.28, size = 229, normalized size = 10.90 \begin {gather*} \frac {c^{14} x^{28 \, n}}{14 \, n} + \frac {b c^{13} x^{27 \, n}}{n} + \frac {13 \, b^{2} c^{12} x^{26 \, n}}{2 \, n} + \frac {26 \, b^{3} c^{11} x^{25 \, n}}{n} + \frac {143 \, b^{4} c^{10} x^{24 \, n}}{2 \, n} + \frac {143 \, b^{5} c^{9} x^{23 \, n}}{n} + \frac {429 \, b^{6} c^{8} x^{22 \, n}}{2 \, n} + \frac {1716 \, b^{7} c^{7} x^{21 \, n}}{7 \, n} + \frac {429 \, b^{8} c^{6} x^{20 \, n}}{2 \, n} + \frac {143 \, b^{9} c^{5} x^{19 \, n}}{n} + \frac {143 \, b^{10} c^{4} x^{18 \, n}}{2 \, n} + \frac {26 \, b^{11} c^{3} x^{17 \, n}}{n} + \frac {13 \, b^{12} c^{2} x^{16 \, n}}{2 \, n} + \frac {b^{13} c x^{15 \, n}}{n} + \frac {b^{14} x^{14 \, n}}{14 \, n} \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. 262 vs.
\(2 (19) = 38\).
time = 0.37, size = 262, normalized size = 12.48 \begin {gather*} \frac {b^{14} x^{14} x^{14 \, n + 14} + 14 \, b^{13} c x^{13} x^{15 \, n + 15} + 91 \, b^{12} c^{2} x^{12} x^{16 \, n + 16} + 364 \, b^{11} c^{3} x^{11} x^{17 \, n + 17} + 1001 \, b^{10} c^{4} x^{10} x^{18 \, n + 18} + 2002 \, b^{9} c^{5} x^{9} x^{19 \, n + 19} + 3003 \, b^{8} c^{6} x^{8} x^{20 \, n + 20} + 3432 \, b^{7} c^{7} x^{7} x^{21 \, n + 21} + 3003 \, b^{6} c^{8} x^{6} x^{22 \, n + 22} + 2002 \, b^{5} c^{9} x^{5} x^{23 \, n + 23} + 1001 \, b^{4} c^{10} x^{4} x^{24 \, n + 24} + 364 \, b^{3} c^{11} x^{3} x^{25 \, n + 25} + 91 \, b^{2} c^{12} x^{2} x^{26 \, n + 26} + 14 \, b c^{13} x x^{27 \, n + 27} + c^{14} x^{28 \, n + 28}}{14 \, n x^{28}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.02, size = 229, normalized size = 10.90 \begin {gather*} \frac {b^{14}\,x^{14\,n}}{14\,n}+\frac {c^{14}\,x^{28\,n}}{14\,n}+\frac {13\,b^{12}\,c^2\,x^{16\,n}}{2\,n}+\frac {26\,b^{11}\,c^3\,x^{17\,n}}{n}+\frac {143\,b^{10}\,c^4\,x^{18\,n}}{2\,n}+\frac {143\,b^9\,c^5\,x^{19\,n}}{n}+\frac {429\,b^8\,c^6\,x^{20\,n}}{2\,n}+\frac {1716\,b^7\,c^7\,x^{21\,n}}{7\,n}+\frac {429\,b^6\,c^8\,x^{22\,n}}{2\,n}+\frac {143\,b^5\,c^9\,x^{23\,n}}{n}+\frac {143\,b^4\,c^{10}\,x^{24\,n}}{2\,n}+\frac {26\,b^3\,c^{11}\,x^{25\,n}}{n}+\frac {13\,b^2\,c^{12}\,x^{26\,n}}{2\,n}+\frac {b^{13}\,c\,x^{15\,n}}{n}+\frac {b\,c^{13}\,x^{27\,n}}{n} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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