Optimal. Leaf size=18 \[ \frac {1}{28} \left (a+b x^2+c x^4\right )^{14} \]
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Rubi [A]
time = 0.21, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {1261, 643}
\begin {gather*} \frac {1}{28} \left (a+b x^2+c x^4\right )^{14} \end {gather*}
Antiderivative was successfully verified.
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Rule 643
Rule 1261
Rubi steps
\begin {align*} \int x \left (b+2 c x^2\right ) \left (a+b x^2+c x^4\right )^{13} \, dx &=\frac {1}{2} \text {Subst}\left (\int (b+2 c x) \left (a+b x+c x^2\right )^{13} \, dx,x,x^2\right )\\ &=\frac {1}{28} \left (a+b x^2+c x^4\right )^{14}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(233\) vs. \(2(18)=36\).
time = 0.12, size = 233, normalized size = 12.94 \begin {gather*} \frac {1}{28} x^2 \left (b+c x^2\right ) \left (14 a^{13}+91 a^{12} x^2 \left (b+c x^2\right )+364 a^{11} x^4 \left (b+c x^2\right )^2+1001 a^{10} x^6 \left (b+c x^2\right )^3+2002 a^9 x^8 \left (b+c x^2\right )^4+3003 a^8 x^{10} \left (b+c x^2\right )^5+3432 a^7 x^{12} \left (b+c x^2\right )^6+3003 a^6 x^{14} \left (b+c x^2\right )^7+2002 a^5 x^{16} \left (b+c x^2\right )^8+1001 a^4 x^{18} \left (b+c x^2\right )^9+364 a^3 x^{20} \left (b+c x^2\right )^{10}+91 a^2 x^{22} \left (b+c x^2\right )^{11}+14 a x^{24} \left (b+c x^2\right )^{12}+x^{26} \left (b+c x^2\right )^{13}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 17, normalized size = 0.94
method | result | size |
default | \(\frac {\left (c \,x^{4}+b \,x^{2}+a \right )^{14}}{28}\) | \(17\) |
gosper | \(\text {Expression too large to display}\) | \(1455\) |
risch | \(\text {Expression too large to display}\) | \(1460\) |
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. 1240 vs.
\(2 (16) = 32\).
time = 0.30, size = 1240, normalized size = 68.89 \begin {gather*} \frac {1}{28} \, c^{14} x^{56} + \frac {1}{2} \, b c^{13} x^{54} + \frac {1}{4} \, {\left (13 \, b^{2} c^{12} + 2 \, a c^{13}\right )} x^{52} + \frac {13}{2} \, {\left (2 \, b^{3} c^{11} + a b c^{12}\right )} x^{50} + \frac {13}{4} \, {\left (11 \, b^{4} c^{10} + 12 \, a b^{2} c^{11} + a^{2} c^{12}\right )} x^{48} + \frac {13}{2} \, {\left (11 \, b^{5} c^{9} + 22 \, a b^{3} c^{10} + 6 \, a^{2} b c^{11}\right )} x^{46} + \frac {13}{4} \, {\left (33 \, b^{6} c^{8} + 110 \, a b^{4} c^{9} + 66 \, a^{2} b^{2} c^{10} + 4 \, a^{3} c^{11}\right )} x^{44} + \frac {143}{14} \, {\left (12 \, b^{7} c^{7} + 63 \, a b^{5} c^{8} + 70 \, a^{2} b^{3} c^{9} + 14 \, a^{3} b c^{10}\right )} x^{42} + \frac {143}{4} \, {\left (3 \, b^{8} c^{6} + 24 \, a b^{6} c^{7} + 45 \, a^{2} b^{4} c^{8} + 20 \, a^{3} b^{2} c^{9} + a^{4} c^{10}\right )} x^{40} + \frac {143}{2} \, {\left (b^{9} c^{5} + 12 \, a b^{7} c^{6} + 36 \, a^{2} b^{5} c^{7} + 30 \, a^{3} b^{3} c^{8} + 5 \, a^{4} b c^{9}\right )} x^{38} + \frac {143}{4} \, {\left (b^{10} c^{4} + 18 \, a b^{8} c^{5} + 84 \, a^{2} b^{6} c^{6} + 120 \, a^{3} b^{4} c^{7} + 45 \, a^{4} b^{2} c^{8} + 2 \, a^{5} c^{9}\right )} x^{36} + \frac {13}{2} \, {\left (2 \, b^{11} c^{3} + 55 \, a b^{9} c^{4} + 396 \, a^{2} b^{7} c^{5} + 924 \, a^{3} b^{5} c^{6} + 660 \, a^{4} b^{3} c^{7} + 99 \, a^{5} b c^{8}\right )} x^{34} + \frac {13}{4} \, {\left (b^{12} c^{2} + 44 \, a b^{10} c^{3} + 495 \, a^{2} b^{8} c^{4} + 1848 \, a^{3} b^{6} c^{5} + 2310 \, a^{4} b^{4} c^{6} + 792 \, a^{5} b^{2} c^{7} + 33 \, a^{6} c^{8}\right )} x^{32} + \frac {1}{2} \, {\left (b^{13} c + 78 \, a b^{11} c^{2} + 1430 \, a^{2} b^{9} c^{3} + 8580 \, a^{3} b^{7} c^{4} + 18018 \, a^{4} b^{5} c^{5} + 12012 \, a^{5} b^{3} c^{6} + 1716 \, a^{6} b c^{7}\right )} x^{30} + \frac {1}{28} \, {\left (b^{14} + 182 \, a b^{12} c + 6006 \, a^{2} b^{10} c^{2} + 60060 \, a^{3} b^{8} c^{3} + 210210 \, a^{4} b^{6} c^{4} + 252252 \, a^{5} b^{4} c^{5} + 84084 \, a^{6} b^{2} c^{6} + 3432 \, a^{7} c^{7}\right )} x^{28} + \frac {1}{2} \, {\left (a b^{13} + 78 \, a^{2} b^{11} c + 1430 \, a^{3} b^{9} c^{2} + 8580 \, a^{4} b^{7} c^{3} + 18018 \, a^{5} b^{5} c^{4} + 12012 \, a^{6} b^{3} c^{5} + 1716 \, a^{7} b c^{6}\right )} x^{26} + \frac {13}{4} \, {\left (a^{2} b^{12} + 44 \, a^{3} b^{10} c + 495 \, a^{4} b^{8} c^{2} + 1848 \, a^{5} b^{6} c^{3} + 2310 \, a^{6} b^{4} c^{4} + 792 \, a^{7} b^{2} c^{5} + 33 \, a^{8} c^{6}\right )} x^{24} + \frac {13}{2} \, {\left (2 \, a^{3} b^{11} + 55 \, a^{4} b^{9} c + 396 \, a^{5} b^{7} c^{2} + 924 \, a^{6} b^{5} c^{3} + 660 \, a^{7} b^{3} c^{4} + 99 \, a^{8} b c^{5}\right )} x^{22} + \frac {143}{4} \, {\left (a^{4} b^{10} + 18 \, a^{5} b^{8} c + 84 \, a^{6} b^{6} c^{2} + 120 \, a^{7} b^{4} c^{3} + 45 \, a^{8} b^{2} c^{4} + 2 \, a^{9} c^{5}\right )} x^{20} + \frac {143}{2} \, {\left (a^{5} b^{9} + 12 \, a^{6} b^{7} c + 36 \, a^{7} b^{5} c^{2} + 30 \, a^{8} b^{3} c^{3} + 5 \, a^{9} b c^{4}\right )} x^{18} + \frac {143}{4} \, {\left (3 \, a^{6} b^{8} + 24 \, a^{7} b^{6} c + 45 \, a^{8} b^{4} c^{2} + 20 \, a^{9} b^{2} c^{3} + a^{10} c^{4}\right )} x^{16} + \frac {1}{2} \, a^{13} b x^{2} + \frac {143}{14} \, {\left (12 \, a^{7} b^{7} + 63 \, a^{8} b^{5} c + 70 \, a^{9} b^{3} c^{2} + 14 \, a^{10} b c^{3}\right )} x^{14} + \frac {13}{4} \, {\left (33 \, a^{8} b^{6} + 110 \, a^{9} b^{4} c + 66 \, a^{10} b^{2} c^{2} + 4 \, a^{11} c^{3}\right )} x^{12} + \frac {13}{2} \, {\left (11 \, a^{9} b^{5} + 22 \, a^{10} b^{3} c + 6 \, a^{11} b c^{2}\right )} x^{10} + \frac {13}{4} \, {\left (11 \, a^{10} b^{4} + 12 \, a^{11} b^{2} c + a^{12} c^{2}\right )} x^{8} + \frac {13}{2} \, {\left (2 \, a^{11} b^{3} + a^{12} b c\right )} x^{6} + \frac {1}{4} \, {\left (13 \, a^{12} b^{2} + 2 \, a^{13} c\right )} x^{4} \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. 1240 vs.
\(2 (16) = 32\).
time = 0.35, size = 1240, normalized size = 68.89 \begin {gather*} \frac {1}{28} \, c^{14} x^{56} + \frac {1}{2} \, b c^{13} x^{54} + \frac {1}{4} \, {\left (13 \, b^{2} c^{12} + 2 \, a c^{13}\right )} x^{52} + \frac {13}{2} \, {\left (2 \, b^{3} c^{11} + a b c^{12}\right )} x^{50} + \frac {13}{4} \, {\left (11 \, b^{4} c^{10} + 12 \, a b^{2} c^{11} + a^{2} c^{12}\right )} x^{48} + \frac {13}{2} \, {\left (11 \, b^{5} c^{9} + 22 \, a b^{3} c^{10} + 6 \, a^{2} b c^{11}\right )} x^{46} + \frac {13}{4} \, {\left (33 \, b^{6} c^{8} + 110 \, a b^{4} c^{9} + 66 \, a^{2} b^{2} c^{10} + 4 \, a^{3} c^{11}\right )} x^{44} + \frac {143}{14} \, {\left (12 \, b^{7} c^{7} + 63 \, a b^{5} c^{8} + 70 \, a^{2} b^{3} c^{9} + 14 \, a^{3} b c^{10}\right )} x^{42} + \frac {143}{4} \, {\left (3 \, b^{8} c^{6} + 24 \, a b^{6} c^{7} + 45 \, a^{2} b^{4} c^{8} + 20 \, a^{3} b^{2} c^{9} + a^{4} c^{10}\right )} x^{40} + \frac {143}{2} \, {\left (b^{9} c^{5} + 12 \, a b^{7} c^{6} + 36 \, a^{2} b^{5} c^{7} + 30 \, a^{3} b^{3} c^{8} + 5 \, a^{4} b c^{9}\right )} x^{38} + \frac {143}{4} \, {\left (b^{10} c^{4} + 18 \, a b^{8} c^{5} + 84 \, a^{2} b^{6} c^{6} + 120 \, a^{3} b^{4} c^{7} + 45 \, a^{4} b^{2} c^{8} + 2 \, a^{5} c^{9}\right )} x^{36} + \frac {13}{2} \, {\left (2 \, b^{11} c^{3} + 55 \, a b^{9} c^{4} + 396 \, a^{2} b^{7} c^{5} + 924 \, a^{3} b^{5} c^{6} + 660 \, a^{4} b^{3} c^{7} + 99 \, a^{5} b c^{8}\right )} x^{34} + \frac {13}{4} \, {\left (b^{12} c^{2} + 44 \, a b^{10} c^{3} + 495 \, a^{2} b^{8} c^{4} + 1848 \, a^{3} b^{6} c^{5} + 2310 \, a^{4} b^{4} c^{6} + 792 \, a^{5} b^{2} c^{7} + 33 \, a^{6} c^{8}\right )} x^{32} + \frac {1}{2} \, {\left (b^{13} c + 78 \, a b^{11} c^{2} + 1430 \, a^{2} b^{9} c^{3} + 8580 \, a^{3} b^{7} c^{4} + 18018 \, a^{4} b^{5} c^{5} + 12012 \, a^{5} b^{3} c^{6} + 1716 \, a^{6} b c^{7}\right )} x^{30} + \frac {1}{28} \, {\left (b^{14} + 182 \, a b^{12} c + 6006 \, a^{2} b^{10} c^{2} + 60060 \, a^{3} b^{8} c^{3} + 210210 \, a^{4} b^{6} c^{4} + 252252 \, a^{5} b^{4} c^{5} + 84084 \, a^{6} b^{2} c^{6} + 3432 \, a^{7} c^{7}\right )} x^{28} + \frac {1}{2} \, {\left (a b^{13} + 78 \, a^{2} b^{11} c + 1430 \, a^{3} b^{9} c^{2} + 8580 \, a^{4} b^{7} c^{3} + 18018 \, a^{5} b^{5} c^{4} + 12012 \, a^{6} b^{3} c^{5} + 1716 \, a^{7} b c^{6}\right )} x^{26} + \frac {13}{4} \, {\left (a^{2} b^{12} + 44 \, a^{3} b^{10} c + 495 \, a^{4} b^{8} c^{2} + 1848 \, a^{5} b^{6} c^{3} + 2310 \, a^{6} b^{4} c^{4} + 792 \, a^{7} b^{2} c^{5} + 33 \, a^{8} c^{6}\right )} x^{24} + \frac {13}{2} \, {\left (2 \, a^{3} b^{11} + 55 \, a^{4} b^{9} c + 396 \, a^{5} b^{7} c^{2} + 924 \, a^{6} b^{5} c^{3} + 660 \, a^{7} b^{3} c^{4} + 99 \, a^{8} b c^{5}\right )} x^{22} + \frac {143}{4} \, {\left (a^{4} b^{10} + 18 \, a^{5} b^{8} c + 84 \, a^{6} b^{6} c^{2} + 120 \, a^{7} b^{4} c^{3} + 45 \, a^{8} b^{2} c^{4} + 2 \, a^{9} c^{5}\right )} x^{20} + \frac {143}{2} \, {\left (a^{5} b^{9} + 12 \, a^{6} b^{7} c + 36 \, a^{7} b^{5} c^{2} + 30 \, a^{8} b^{3} c^{3} + 5 \, a^{9} b c^{4}\right )} x^{18} + \frac {143}{4} \, {\left (3 \, a^{6} b^{8} + 24 \, a^{7} b^{6} c + 45 \, a^{8} b^{4} c^{2} + 20 \, a^{9} b^{2} c^{3} + a^{10} c^{4}\right )} x^{16} + \frac {1}{2} \, a^{13} b x^{2} + \frac {143}{14} \, {\left (12 \, a^{7} b^{7} + 63 \, a^{8} b^{5} c + 70 \, a^{9} b^{3} c^{2} + 14 \, a^{10} b c^{3}\right )} x^{14} + \frac {13}{4} \, {\left (33 \, a^{8} b^{6} + 110 \, a^{9} b^{4} c + 66 \, a^{10} b^{2} c^{2} + 4 \, a^{11} c^{3}\right )} x^{12} + \frac {13}{2} \, {\left (11 \, a^{9} b^{5} + 22 \, a^{10} b^{3} c + 6 \, a^{11} b c^{2}\right )} x^{10} + \frac {13}{4} \, {\left (11 \, a^{10} b^{4} + 12 \, a^{11} b^{2} c + a^{12} c^{2}\right )} x^{8} + \frac {13}{2} \, {\left (2 \, a^{11} b^{3} + a^{12} b c\right )} x^{6} + \frac {1}{4} \, {\left (13 \, a^{12} b^{2} + 2 \, a^{13} c\right )} x^{4} \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. 1384 vs.
\(2 (14) = 28\).
time = 0.17, size = 1384, normalized size = 76.89 \begin {gather*} \frac {a^{13} b x^{2}}{2} + \frac {b c^{13} x^{54}}{2} + \frac {c^{14} x^{56}}{28} + x^{52} \left (\frac {a c^{13}}{2} + \frac {13 b^{2} c^{12}}{4}\right ) + x^{50} \cdot \left (\frac {13 a b c^{12}}{2} + 13 b^{3} c^{11}\right ) + x^{48} \cdot \left (\frac {13 a^{2} c^{12}}{4} + 39 a b^{2} c^{11} + \frac {143 b^{4} c^{10}}{4}\right ) + x^{46} \cdot \left (39 a^{2} b c^{11} + 143 a b^{3} c^{10} + \frac {143 b^{5} c^{9}}{2}\right ) + x^{44} \cdot \left (13 a^{3} c^{11} + \frac {429 a^{2} b^{2} c^{10}}{2} + \frac {715 a b^{4} c^{9}}{2} + \frac {429 b^{6} c^{8}}{4}\right ) + x^{42} \cdot \left (143 a^{3} b c^{10} + 715 a^{2} b^{3} c^{9} + \frac {1287 a b^{5} c^{8}}{2} + \frac {858 b^{7} c^{7}}{7}\right ) + x^{40} \cdot \left (\frac {143 a^{4} c^{10}}{4} + 715 a^{3} b^{2} c^{9} + \frac {6435 a^{2} b^{4} c^{8}}{4} + 858 a b^{6} c^{7} + \frac {429 b^{8} c^{6}}{4}\right ) + x^{38} \cdot \left (\frac {715 a^{4} b c^{9}}{2} + 2145 a^{3} b^{3} c^{8} + 2574 a^{2} b^{5} c^{7} + 858 a b^{7} c^{6} + \frac {143 b^{9} c^{5}}{2}\right ) + x^{36} \cdot \left (\frac {143 a^{5} c^{9}}{2} + \frac {6435 a^{4} b^{2} c^{8}}{4} + 4290 a^{3} b^{4} c^{7} + 3003 a^{2} b^{6} c^{6} + \frac {1287 a b^{8} c^{5}}{2} + \frac {143 b^{10} c^{4}}{4}\right ) + x^{34} \cdot \left (\frac {1287 a^{5} b c^{8}}{2} + 4290 a^{4} b^{3} c^{7} + 6006 a^{3} b^{5} c^{6} + 2574 a^{2} b^{7} c^{5} + \frac {715 a b^{9} c^{4}}{2} + 13 b^{11} c^{3}\right ) + x^{32} \cdot \left (\frac {429 a^{6} c^{8}}{4} + 2574 a^{5} b^{2} c^{7} + \frac {15015 a^{4} b^{4} c^{6}}{2} + 6006 a^{3} b^{6} c^{5} + \frac {6435 a^{2} b^{8} c^{4}}{4} + 143 a b^{10} c^{3} + \frac {13 b^{12} c^{2}}{4}\right ) + x^{30} \cdot \left (858 a^{6} b c^{7} + 6006 a^{5} b^{3} c^{6} + 9009 a^{4} b^{5} c^{5} + 4290 a^{3} b^{7} c^{4} + 715 a^{2} b^{9} c^{3} + 39 a b^{11} c^{2} + \frac {b^{13} c}{2}\right ) + x^{28} \cdot \left (\frac {858 a^{7} c^{7}}{7} + 3003 a^{6} b^{2} c^{6} + 9009 a^{5} b^{4} c^{5} + \frac {15015 a^{4} b^{6} c^{4}}{2} + 2145 a^{3} b^{8} c^{3} + \frac {429 a^{2} b^{10} c^{2}}{2} + \frac {13 a b^{12} c}{2} + \frac {b^{14}}{28}\right ) + x^{26} \cdot \left (858 a^{7} b c^{6} + 6006 a^{6} b^{3} c^{5} + 9009 a^{5} b^{5} c^{4} + 4290 a^{4} b^{7} c^{3} + 715 a^{3} b^{9} c^{2} + 39 a^{2} b^{11} c + \frac {a b^{13}}{2}\right ) + x^{24} \cdot \left (\frac {429 a^{8} c^{6}}{4} + 2574 a^{7} b^{2} c^{5} + \frac {15015 a^{6} b^{4} c^{4}}{2} + 6006 a^{5} b^{6} c^{3} + \frac {6435 a^{4} b^{8} c^{2}}{4} + 143 a^{3} b^{10} c + \frac {13 a^{2} b^{12}}{4}\right ) + x^{22} \cdot \left (\frac {1287 a^{8} b c^{5}}{2} + 4290 a^{7} b^{3} c^{4} + 6006 a^{6} b^{5} c^{3} + 2574 a^{5} b^{7} c^{2} + \frac {715 a^{4} b^{9} c}{2} + 13 a^{3} b^{11}\right ) + x^{20} \cdot \left (\frac {143 a^{9} c^{5}}{2} + \frac {6435 a^{8} b^{2} c^{4}}{4} + 4290 a^{7} b^{4} c^{3} + 3003 a^{6} b^{6} c^{2} + \frac {1287 a^{5} b^{8} c}{2} + \frac {143 a^{4} b^{10}}{4}\right ) + x^{18} \cdot \left (\frac {715 a^{9} b c^{4}}{2} + 2145 a^{8} b^{3} c^{3} + 2574 a^{7} b^{5} c^{2} + 858 a^{6} b^{7} c + \frac {143 a^{5} b^{9}}{2}\right ) + x^{16} \cdot \left (\frac {143 a^{10} c^{4}}{4} + 715 a^{9} b^{2} c^{3} + \frac {6435 a^{8} b^{4} c^{2}}{4} + 858 a^{7} b^{6} c + \frac {429 a^{6} b^{8}}{4}\right ) + x^{14} \cdot \left (143 a^{10} b c^{3} + 715 a^{9} b^{3} c^{2} + \frac {1287 a^{8} b^{5} c}{2} + \frac {858 a^{7} b^{7}}{7}\right ) + x^{12} \cdot \left (13 a^{11} c^{3} + \frac {429 a^{10} b^{2} c^{2}}{2} + \frac {715 a^{9} b^{4} c}{2} + \frac {429 a^{8} b^{6}}{4}\right ) + x^{10} \cdot \left (39 a^{11} b c^{2} + 143 a^{10} b^{3} c + \frac {143 a^{9} b^{5}}{2}\right ) + x^{8} \cdot \left (\frac {13 a^{12} c^{2}}{4} + 39 a^{11} b^{2} c + \frac {143 a^{10} b^{4}}{4}\right ) + x^{6} \cdot \left (\frac {13 a^{12} b c}{2} + 13 a^{11} b^{3}\right ) + x^{4} \left (\frac {a^{13} c}{2} + \frac {13 a^{12} b^{2}}{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 246 vs.
\(2 (16) = 32\).
time = 3.60, size = 246, normalized size = 13.67 \begin {gather*} \frac {1}{28} \, {\left (c x^{4} + b x^{2}\right )}^{14} + \frac {1}{2} \, {\left (c x^{4} + b x^{2}\right )}^{13} a + \frac {13}{4} \, {\left (c x^{4} + b x^{2}\right )}^{12} a^{2} + 13 \, {\left (c x^{4} + b x^{2}\right )}^{11} a^{3} + \frac {143}{4} \, {\left (c x^{4} + b x^{2}\right )}^{10} a^{4} + \frac {143}{2} \, {\left (c x^{4} + b x^{2}\right )}^{9} a^{5} + \frac {429}{4} \, {\left (c x^{4} + b x^{2}\right )}^{8} a^{6} + \frac {858}{7} \, {\left (c x^{4} + b x^{2}\right )}^{7} a^{7} + \frac {429}{4} \, {\left (c x^{4} + b x^{2}\right )}^{6} a^{8} + \frac {143}{2} \, {\left (c x^{4} + b x^{2}\right )}^{5} a^{9} + \frac {143}{4} \, {\left (c x^{4} + b x^{2}\right )}^{4} a^{10} + 13 \, {\left (c x^{4} + b x^{2}\right )}^{3} a^{11} + \frac {13}{4} \, {\left (c x^{4} + b x^{2}\right )}^{2} a^{12} + \frac {1}{2} \, {\left (c x^{4} + b x^{2}\right )} a^{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.23, size = 1210, normalized size = 67.22 \begin {gather*} x^{24}\,\left (\frac {429\,a^8\,c^6}{4}+2574\,a^7\,b^2\,c^5+\frac {15015\,a^6\,b^4\,c^4}{2}+6006\,a^5\,b^6\,c^3+\frac {6435\,a^4\,b^8\,c^2}{4}+143\,a^3\,b^{10}\,c+\frac {13\,a^2\,b^{12}}{4}\right )+x^{32}\,\left (\frac {429\,a^6\,c^8}{4}+2574\,a^5\,b^2\,c^7+\frac {15015\,a^4\,b^4\,c^6}{2}+6006\,a^3\,b^6\,c^5+\frac {6435\,a^2\,b^8\,c^4}{4}+143\,a\,b^{10}\,c^3+\frac {13\,b^{12}\,c^2}{4}\right )+x^{26}\,\left (858\,a^7\,b\,c^6+6006\,a^6\,b^3\,c^5+9009\,a^5\,b^5\,c^4+4290\,a^4\,b^7\,c^3+715\,a^3\,b^9\,c^2+39\,a^2\,b^{11}\,c+\frac {a\,b^{13}}{2}\right )+x^{30}\,\left (858\,a^6\,b\,c^7+6006\,a^5\,b^3\,c^6+9009\,a^4\,b^5\,c^5+4290\,a^3\,b^7\,c^4+715\,a^2\,b^9\,c^3+39\,a\,b^{11}\,c^2+\frac {b^{13}\,c}{2}\right )+x^{12}\,\left (13\,a^{11}\,c^3+\frac {429\,a^{10}\,b^2\,c^2}{2}+\frac {715\,a^9\,b^4\,c}{2}+\frac {429\,a^8\,b^6}{4}\right )+x^{44}\,\left (13\,a^3\,c^{11}+\frac {429\,a^2\,b^2\,c^{10}}{2}+\frac {715\,a\,b^4\,c^9}{2}+\frac {429\,b^6\,c^8}{4}\right )+x^{20}\,\left (\frac {143\,a^9\,c^5}{2}+\frac {6435\,a^8\,b^2\,c^4}{4}+4290\,a^7\,b^4\,c^3+3003\,a^6\,b^6\,c^2+\frac {1287\,a^5\,b^8\,c}{2}+\frac {143\,a^4\,b^{10}}{4}\right )+x^{36}\,\left (\frac {143\,a^5\,c^9}{2}+\frac {6435\,a^4\,b^2\,c^8}{4}+4290\,a^3\,b^4\,c^7+3003\,a^2\,b^6\,c^6+\frac {1287\,a\,b^8\,c^5}{2}+\frac {143\,b^{10}\,c^4}{4}\right )+x^{28}\,\left (\frac {858\,a^7\,c^7}{7}+3003\,a^6\,b^2\,c^6+9009\,a^5\,b^4\,c^5+\frac {15015\,a^4\,b^6\,c^4}{2}+2145\,a^3\,b^8\,c^3+\frac {429\,a^2\,b^{10}\,c^2}{2}+\frac {13\,a\,b^{12}\,c}{2}+\frac {b^{14}}{28}\right )+x^{16}\,\left (\frac {143\,a^{10}\,c^4}{4}+715\,a^9\,b^2\,c^3+\frac {6435\,a^8\,b^4\,c^2}{4}+858\,a^7\,b^6\,c+\frac {429\,a^6\,b^8}{4}\right )+x^{40}\,\left (\frac {143\,a^4\,c^{10}}{4}+715\,a^3\,b^2\,c^9+\frac {6435\,a^2\,b^4\,c^8}{4}+858\,a\,b^6\,c^7+\frac {429\,b^8\,c^6}{4}\right )+\frac {c^{14}\,x^{56}}{28}+x^4\,\left (\frac {c\,a^{13}}{2}+\frac {13\,a^{12}\,b^2}{4}\right )+\frac {13\,a^{10}\,x^8\,\left (a^2\,c^2+12\,a\,b^2\,c+11\,b^4\right )}{4}+\frac {13\,c^{10}\,x^{48}\,\left (a^2\,c^2+12\,a\,b^2\,c+11\,b^4\right )}{4}+\frac {a^{13}\,b\,x^2}{2}+\frac {b\,c^{13}\,x^{54}}{2}+\frac {c^{12}\,x^{52}\,\left (13\,b^2+2\,a\,c\right )}{4}+\frac {143\,a^7\,b\,x^{14}\,\left (14\,a^3\,c^3+70\,a^2\,b^2\,c^2+63\,a\,b^4\,c+12\,b^6\right )}{14}+\frac {143\,b\,c^7\,x^{42}\,\left (14\,a^3\,c^3+70\,a^2\,b^2\,c^2+63\,a\,b^4\,c+12\,b^6\right )}{14}+\frac {143\,a^5\,b\,x^{18}\,\left (5\,a^4\,c^4+30\,a^3\,b^2\,c^3+36\,a^2\,b^4\,c^2+12\,a\,b^6\,c+b^8\right )}{2}+\frac {143\,b\,c^5\,x^{38}\,\left (5\,a^4\,c^4+30\,a^3\,b^2\,c^3+36\,a^2\,b^4\,c^2+12\,a\,b^6\,c+b^8\right )}{2}+\frac {13\,a^3\,b\,x^{22}\,\left (99\,a^5\,c^5+660\,a^4\,b^2\,c^4+924\,a^3\,b^4\,c^3+396\,a^2\,b^6\,c^2+55\,a\,b^8\,c+2\,b^{10}\right )}{2}+\frac {13\,b\,c^3\,x^{34}\,\left (99\,a^5\,c^5+660\,a^4\,b^2\,c^4+924\,a^3\,b^4\,c^3+396\,a^2\,b^6\,c^2+55\,a\,b^8\,c+2\,b^{10}\right )}{2}+\frac {13\,a^9\,b\,x^{10}\,\left (6\,a^2\,c^2+22\,a\,b^2\,c+11\,b^4\right )}{2}+\frac {13\,b\,c^9\,x^{46}\,\left (6\,a^2\,c^2+22\,a\,b^2\,c+11\,b^4\right )}{2}+\frac {13\,a^{11}\,b\,x^6\,\left (2\,b^2+a\,c\right )}{2}+\frac {13\,b\,c^{11}\,x^{50}\,\left (2\,b^2+a\,c\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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