Optimal. Leaf size=72 \[ -\frac {A (a+b x)^{11}}{13 a x^{13}}+\frac {(2 A b-13 a B) (a+b x)^{11}}{156 a^2 x^{12}}-\frac {b (2 A b-13 a B) (a+b x)^{11}}{1716 a^3 x^{11}} \]
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Rubi [A]
time = 0.02, antiderivative size = 72, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {79, 47, 37}
\begin {gather*} -\frac {b (a+b x)^{11} (2 A b-13 a B)}{1716 a^3 x^{11}}+\frac {(a+b x)^{11} (2 A b-13 a B)}{156 a^2 x^{12}}-\frac {A (a+b x)^{11}}{13 a x^{13}} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 47
Rule 79
Rubi steps
\begin {align*} \int \frac {(a+b x)^{10} (A+B x)}{x^{14}} \, dx &=-\frac {A (a+b x)^{11}}{13 a x^{13}}+\frac {(-2 A b+13 a B) \int \frac {(a+b x)^{10}}{x^{13}} \, dx}{13 a}\\ &=-\frac {A (a+b x)^{11}}{13 a x^{13}}+\frac {(2 A b-13 a B) (a+b x)^{11}}{156 a^2 x^{12}}+\frac {(b (2 A b-13 a B)) \int \frac {(a+b x)^{10}}{x^{12}} \, dx}{156 a^2}\\ &=-\frac {A (a+b x)^{11}}{13 a x^{13}}+\frac {(2 A b-13 a B) (a+b x)^{11}}{156 a^2 x^{12}}-\frac {b (2 A b-13 a B) (a+b x)^{11}}{1716 a^3 x^{11}}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(202\) vs. \(2(72)=144\).
time = 0.05, size = 202, normalized size = 2.81 \begin {gather*} -\frac {286 b^{10} x^{10} (2 A+3 B x)+1430 a b^9 x^9 (3 A+4 B x)+3861 a^2 b^8 x^8 (4 A+5 B x)+6864 a^3 b^7 x^7 (5 A+6 B x)+8580 a^4 b^6 x^6 (6 A+7 B x)+7722 a^5 b^5 x^5 (7 A+8 B x)+5005 a^6 b^4 x^4 (8 A+9 B x)+2288 a^7 b^3 x^3 (9 A+10 B x)+702 a^8 b^2 x^2 (10 A+11 B x)+130 a^9 b x (11 A+12 B x)+11 a^{10} (12 A+13 B x)}{1716 x^{13}} \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. \(207\) vs.
\(2(66)=132\).
time = 0.07, size = 208, normalized size = 2.89
method | result | size |
default | \(-\frac {10 a^{6} b^{3} \left (7 A b +4 B a \right )}{3 x^{9}}-\frac {5 a^{8} b \left (9 A b +2 B a \right )}{11 x^{11}}-\frac {3 a^{2} b^{7} \left (3 A b +8 B a \right )}{x^{5}}-\frac {a^{9} \left (10 A b +B a \right )}{12 x^{12}}-\frac {5 a \,b^{8} \left (2 A b +9 B a \right )}{4 x^{4}}-\frac {5 a^{3} b^{6} \left (4 A b +7 B a \right )}{x^{6}}-\frac {3 a^{7} b^{2} \left (8 A b +3 B a \right )}{2 x^{10}}-\frac {b^{10} B}{2 x^{2}}-\frac {a^{10} A}{13 x^{13}}-\frac {b^{9} \left (A b +10 B a \right )}{3 x^{3}}-\frac {21 a^{5} b^{4} \left (6 A b +5 B a \right )}{4 x^{8}}-\frac {6 a^{4} b^{5} \left (5 A b +6 B a \right )}{x^{7}}\) | \(208\) |
norman | \(\frac {-\frac {b^{10} B \,x^{11}}{2}+\left (-\frac {1}{3} b^{10} A -\frac {10}{3} a \,b^{9} B \right ) x^{10}+\left (-\frac {5}{2} a \,b^{9} A -\frac {45}{4} a^{2} b^{8} B \right ) x^{9}+\left (-9 a^{2} b^{8} A -24 a^{3} b^{7} B \right ) x^{8}+\left (-20 a^{3} b^{7} A -35 a^{4} b^{6} B \right ) x^{7}+\left (-30 a^{4} b^{6} A -36 a^{5} b^{5} B \right ) x^{6}+\left (-\frac {63}{2} a^{5} b^{5} A -\frac {105}{4} a^{6} b^{4} B \right ) x^{5}+\left (-\frac {70}{3} a^{6} b^{4} A -\frac {40}{3} a^{7} b^{3} B \right ) x^{4}+\left (-12 a^{7} b^{3} A -\frac {9}{2} a^{8} b^{2} B \right ) x^{3}+\left (-\frac {45}{11} a^{8} b^{2} A -\frac {10}{11} a^{9} b B \right ) x^{2}+\left (-\frac {5}{6} a^{9} b A -\frac {1}{12} a^{10} B \right ) x -\frac {a^{10} A}{13}}{x^{13}}\) | \(235\) |
risch | \(\frac {-\frac {b^{10} B \,x^{11}}{2}+\left (-\frac {1}{3} b^{10} A -\frac {10}{3} a \,b^{9} B \right ) x^{10}+\left (-\frac {5}{2} a \,b^{9} A -\frac {45}{4} a^{2} b^{8} B \right ) x^{9}+\left (-9 a^{2} b^{8} A -24 a^{3} b^{7} B \right ) x^{8}+\left (-20 a^{3} b^{7} A -35 a^{4} b^{6} B \right ) x^{7}+\left (-30 a^{4} b^{6} A -36 a^{5} b^{5} B \right ) x^{6}+\left (-\frac {63}{2} a^{5} b^{5} A -\frac {105}{4} a^{6} b^{4} B \right ) x^{5}+\left (-\frac {70}{3} a^{6} b^{4} A -\frac {40}{3} a^{7} b^{3} B \right ) x^{4}+\left (-12 a^{7} b^{3} A -\frac {9}{2} a^{8} b^{2} B \right ) x^{3}+\left (-\frac {45}{11} a^{8} b^{2} A -\frac {10}{11} a^{9} b B \right ) x^{2}+\left (-\frac {5}{6} a^{9} b A -\frac {1}{12} a^{10} B \right ) x -\frac {a^{10} A}{13}}{x^{13}}\) | \(235\) |
gosper | \(-\frac {858 b^{10} B \,x^{11}+572 A \,b^{10} x^{10}+5720 B a \,b^{9} x^{10}+4290 a A \,b^{9} x^{9}+19305 B \,a^{2} b^{8} x^{9}+15444 a^{2} A \,b^{8} x^{8}+41184 B \,a^{3} b^{7} x^{8}+34320 a^{3} A \,b^{7} x^{7}+60060 B \,a^{4} b^{6} x^{7}+51480 a^{4} A \,b^{6} x^{6}+61776 B \,a^{5} b^{5} x^{6}+54054 a^{5} A \,b^{5} x^{5}+45045 B \,a^{6} b^{4} x^{5}+40040 a^{6} A \,b^{4} x^{4}+22880 B \,a^{7} b^{3} x^{4}+20592 a^{7} A \,b^{3} x^{3}+7722 B \,a^{8} b^{2} x^{3}+7020 a^{8} A \,b^{2} x^{2}+1560 B \,a^{9} b \,x^{2}+1430 a^{9} A b x +143 a^{10} B x +132 a^{10} A}{1716 x^{13}}\) | \(244\) |
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. 243 vs.
\(2 (66) = 132\).
time = 0.28, size = 243, normalized size = 3.38 \begin {gather*} -\frac {858 \, B b^{10} x^{11} + 132 \, A a^{10} + 572 \, {\left (10 \, B a b^{9} + A b^{10}\right )} x^{10} + 2145 \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{9} + 5148 \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{8} + 8580 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{7} + 10296 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{6} + 9009 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{5} + 5720 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{4} + 2574 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{3} + 780 \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{2} + 143 \, {\left (B a^{10} + 10 \, A a^{9} b\right )} x}{1716 \, x^{13}} \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. 243 vs.
\(2 (66) = 132\).
time = 0.60, size = 243, normalized size = 3.38 \begin {gather*} -\frac {858 \, B b^{10} x^{11} + 132 \, A a^{10} + 572 \, {\left (10 \, B a b^{9} + A b^{10}\right )} x^{10} + 2145 \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{9} + 5148 \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{8} + 8580 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{7} + 10296 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{6} + 9009 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{5} + 5720 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{4} + 2574 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{3} + 780 \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{2} + 143 \, {\left (B a^{10} + 10 \, A a^{9} b\right )} x}{1716 \, x^{13}} \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. 260 vs.
\(2 (65) = 130\).
time = 130.21, size = 260, normalized size = 3.61 \begin {gather*} \frac {- 132 A a^{10} - 858 B b^{10} x^{11} + x^{10} \left (- 572 A b^{10} - 5720 B a b^{9}\right ) + x^{9} \left (- 4290 A a b^{9} - 19305 B a^{2} b^{8}\right ) + x^{8} \left (- 15444 A a^{2} b^{8} - 41184 B a^{3} b^{7}\right ) + x^{7} \left (- 34320 A a^{3} b^{7} - 60060 B a^{4} b^{6}\right ) + x^{6} \left (- 51480 A a^{4} b^{6} - 61776 B a^{5} b^{5}\right ) + x^{5} \left (- 54054 A a^{5} b^{5} - 45045 B a^{6} b^{4}\right ) + x^{4} \left (- 40040 A a^{6} b^{4} - 22880 B a^{7} b^{3}\right ) + x^{3} \left (- 20592 A a^{7} b^{3} - 7722 B a^{8} b^{2}\right ) + x^{2} \left (- 7020 A a^{8} b^{2} - 1560 B a^{9} b\right ) + x \left (- 1430 A a^{9} b - 143 B a^{10}\right )}{1716 x^{13}} \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. 243 vs.
\(2 (66) = 132\).
time = 1.67, size = 243, normalized size = 3.38 \begin {gather*} -\frac {858 \, B b^{10} x^{11} + 5720 \, B a b^{9} x^{10} + 572 \, A b^{10} x^{10} + 19305 \, B a^{2} b^{8} x^{9} + 4290 \, A a b^{9} x^{9} + 41184 \, B a^{3} b^{7} x^{8} + 15444 \, A a^{2} b^{8} x^{8} + 60060 \, B a^{4} b^{6} x^{7} + 34320 \, A a^{3} b^{7} x^{7} + 61776 \, B a^{5} b^{5} x^{6} + 51480 \, A a^{4} b^{6} x^{6} + 45045 \, B a^{6} b^{4} x^{5} + 54054 \, A a^{5} b^{5} x^{5} + 22880 \, B a^{7} b^{3} x^{4} + 40040 \, A a^{6} b^{4} x^{4} + 7722 \, B a^{8} b^{2} x^{3} + 20592 \, A a^{7} b^{3} x^{3} + 1560 \, B a^{9} b x^{2} + 7020 \, A a^{8} b^{2} x^{2} + 143 \, B a^{10} x + 1430 \, A a^{9} b x + 132 \, A a^{10}}{1716 \, x^{13}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.41, size = 235, normalized size = 3.26 \begin {gather*} -\frac {x\,\left (\frac {B\,a^{10}}{12}+\frac {5\,A\,b\,a^9}{6}\right )+\frac {A\,a^{10}}{13}+x^9\,\left (\frac {45\,B\,a^2\,b^8}{4}+\frac {5\,A\,a\,b^9}{2}\right )+x^2\,\left (\frac {10\,B\,a^9\,b}{11}+\frac {45\,A\,a^8\,b^2}{11}\right )+x^{10}\,\left (\frac {A\,b^{10}}{3}+\frac {10\,B\,a\,b^9}{3}\right )+x^3\,\left (\frac {9\,B\,a^8\,b^2}{2}+12\,A\,a^7\,b^3\right )+x^8\,\left (24\,B\,a^3\,b^7+9\,A\,a^2\,b^8\right )+x^7\,\left (35\,B\,a^4\,b^6+20\,A\,a^3\,b^7\right )+x^6\,\left (36\,B\,a^5\,b^5+30\,A\,a^4\,b^6\right )+x^4\,\left (\frac {40\,B\,a^7\,b^3}{3}+\frac {70\,A\,a^6\,b^4}{3}\right )+x^5\,\left (\frac {105\,B\,a^6\,b^4}{4}+\frac {63\,A\,a^5\,b^5}{2}\right )+\frac {B\,b^{10}\,x^{11}}{2}}{x^{13}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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