Optimal. Leaf size=17 \[ -\frac {(a+b x)^{11}}{11 a x^{11}} \]
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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {37}
\begin {gather*} -\frac {(a+b x)^{11}}{11 a x^{11}} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {(a+b x)^{10}}{x^{12}} \, dx &=-\frac {(a+b x)^{11}}{11 a x^{11}}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(114\) vs. \(2(17)=34\).
time = 0.01, size = 114, normalized size = 6.71 \begin {gather*} -\frac {a^{10}}{11 x^{11}}-\frac {a^9 b}{x^{10}}-\frac {5 a^8 b^2}{x^9}-\frac {15 a^7 b^3}{x^8}-\frac {30 a^6 b^4}{x^7}-\frac {42 a^5 b^5}{x^6}-\frac {42 a^4 b^6}{x^5}-\frac {30 a^3 b^7}{x^4}-\frac {15 a^2 b^8}{x^3}-\frac {5 a b^9}{x^2}-\frac {b^{10}}{x} \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. \(112\) vs.
\(2(15)=30\).
time = 0.08, size = 113, normalized size = 6.65
method | result | size |
gosper | \(-\frac {11 b^{10} x^{10}+55 a \,b^{9} x^{9}+165 a^{2} b^{8} x^{8}+330 a^{3} b^{7} x^{7}+462 a^{4} b^{6} x^{6}+462 a^{5} b^{5} x^{5}+330 a^{6} b^{4} x^{4}+165 a^{7} b^{3} x^{3}+55 a^{8} b^{2} x^{2}+11 a^{9} b x +a^{10}}{11 x^{11}}\) | \(111\) |
norman | \(\frac {-b^{10} x^{10}-5 a \,b^{9} x^{9}-15 a^{2} b^{8} x^{8}-30 a^{3} b^{7} x^{7}-42 a^{4} b^{6} x^{6}-42 a^{5} b^{5} x^{5}-30 a^{6} b^{4} x^{4}-15 a^{7} b^{3} x^{3}-5 a^{8} b^{2} x^{2}-a^{9} b x -\frac {1}{11} a^{10}}{x^{11}}\) | \(112\) |
risch | \(\frac {-b^{10} x^{10}-5 a \,b^{9} x^{9}-15 a^{2} b^{8} x^{8}-30 a^{3} b^{7} x^{7}-42 a^{4} b^{6} x^{6}-42 a^{5} b^{5} x^{5}-30 a^{6} b^{4} x^{4}-15 a^{7} b^{3} x^{3}-5 a^{8} b^{2} x^{2}-a^{9} b x -\frac {1}{11} a^{10}}{x^{11}}\) | \(112\) |
default | \(-\frac {a^{9} b}{x^{10}}-\frac {a^{10}}{11 x^{11}}-\frac {b^{10}}{x}-\frac {15 a^{2} b^{8}}{x^{3}}-\frac {30 a^{3} b^{7}}{x^{4}}-\frac {5 a^{8} b^{2}}{x^{9}}-\frac {5 a \,b^{9}}{x^{2}}-\frac {15 a^{7} b^{3}}{x^{8}}-\frac {42 a^{4} b^{6}}{x^{5}}-\frac {42 a^{5} b^{5}}{x^{6}}-\frac {30 a^{6} b^{4}}{x^{7}}\) | \(113\) |
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. 110 vs.
\(2 (15) = 30\).
time = 0.29, size = 110, normalized size = 6.47 \begin {gather*} -\frac {11 \, b^{10} x^{10} + 55 \, a b^{9} x^{9} + 165 \, a^{2} b^{8} x^{8} + 330 \, a^{3} b^{7} x^{7} + 462 \, a^{4} b^{6} x^{6} + 462 \, a^{5} b^{5} x^{5} + 330 \, a^{6} b^{4} x^{4} + 165 \, a^{7} b^{3} x^{3} + 55 \, a^{8} b^{2} x^{2} + 11 \, a^{9} b x + a^{10}}{11 \, x^{11}} \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. 110 vs.
\(2 (15) = 30\).
time = 0.53, size = 110, normalized size = 6.47 \begin {gather*} -\frac {11 \, b^{10} x^{10} + 55 \, a b^{9} x^{9} + 165 \, a^{2} b^{8} x^{8} + 330 \, a^{3} b^{7} x^{7} + 462 \, a^{4} b^{6} x^{6} + 462 \, a^{5} b^{5} x^{5} + 330 \, a^{6} b^{4} x^{4} + 165 \, a^{7} b^{3} x^{3} + 55 \, a^{8} b^{2} x^{2} + 11 \, a^{9} b x + a^{10}}{11 \, x^{11}} \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. 119 vs.
\(2 (14) = 28\).
time = 0.40, size = 119, normalized size = 7.00 \begin {gather*} \frac {- a^{10} - 11 a^{9} b x - 55 a^{8} b^{2} x^{2} - 165 a^{7} b^{3} x^{3} - 330 a^{6} b^{4} x^{4} - 462 a^{5} b^{5} x^{5} - 462 a^{4} b^{6} x^{6} - 330 a^{3} b^{7} x^{7} - 165 a^{2} b^{8} x^{8} - 55 a b^{9} x^{9} - 11 b^{10} x^{10}}{11 x^{11}} \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. 110 vs.
\(2 (15) = 30\).
time = 1.05, size = 110, normalized size = 6.47 \begin {gather*} -\frac {11 \, b^{10} x^{10} + 55 \, a b^{9} x^{9} + 165 \, a^{2} b^{8} x^{8} + 330 \, a^{3} b^{7} x^{7} + 462 \, a^{4} b^{6} x^{6} + 462 \, a^{5} b^{5} x^{5} + 330 \, a^{6} b^{4} x^{4} + 165 \, a^{7} b^{3} x^{3} + 55 \, a^{8} b^{2} x^{2} + 11 \, a^{9} b x + a^{10}}{11 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.13, size = 110, normalized size = 6.47 \begin {gather*} -\frac {\frac {a^{10}}{11}+a^9\,b\,x+5\,a^8\,b^2\,x^2+15\,a^7\,b^3\,x^3+30\,a^6\,b^4\,x^4+42\,a^5\,b^5\,x^5+42\,a^4\,b^6\,x^6+30\,a^3\,b^7\,x^7+15\,a^2\,b^8\,x^8+5\,a\,b^9\,x^9+b^{10}\,x^{10}}{x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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