Optimal. Leaf size=25 \[ -\frac {(1+x)^{12}}{13 x^{13}}+\frac {(1+x)^{12}}{156 x^{12}} \]
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Rubi [A]
time = 0.00, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {27, 47, 37}
\begin {gather*} \frac {(x+1)^{12}}{156 x^{12}}-\frac {(x+1)^{12}}{13 x^{13}} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 37
Rule 47
Rubi steps
\begin {align*} \int \frac {(1+x) \left (1+2 x+x^2\right )^5}{x^{14}} \, dx &=\int \frac {(1+x)^{11}}{x^{14}} \, dx\\ &=-\frac {(1+x)^{12}}{13 x^{13}}-\frac {1}{13} \int \frac {(1+x)^{11}}{x^{13}} \, dx\\ &=-\frac {(1+x)^{12}}{13 x^{13}}+\frac {(1+x)^{12}}{156 x^{12}}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(25)=50\).
time = 0.00, size = 77, normalized size = 3.08 \begin {gather*} -\frac {1}{13 x^{13}}-\frac {11}{12 x^{12}}-\frac {5}{x^{11}}-\frac {33}{2 x^{10}}-\frac {110}{3 x^9}-\frac {231}{4 x^8}-\frac {66}{x^7}-\frac {55}{x^6}-\frac {33}{x^5}-\frac {55}{4 x^4}-\frac {11}{3 x^3}-\frac {1}{2 x^2} \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. \(61\) vs.
\(2(21)=42\).
time = 0.60, size = 62, normalized size = 2.48
method | result | size |
norman | \(\frac {-\frac {1}{2} x^{11}-\frac {11}{3} x^{10}-\frac {55}{4} x^{9}-33 x^{8}-55 x^{7}-66 x^{6}-\frac {231}{4} x^{5}-\frac {110}{3} x^{4}-\frac {33}{2} x^{3}-5 x^{2}-\frac {11}{12} x -\frac {1}{13}}{x^{13}}\) | \(60\) |
risch | \(\frac {-\frac {1}{2} x^{11}-\frac {11}{3} x^{10}-\frac {55}{4} x^{9}-33 x^{8}-55 x^{7}-66 x^{6}-\frac {231}{4} x^{5}-\frac {110}{3} x^{4}-\frac {33}{2} x^{3}-5 x^{2}-\frac {11}{12} x -\frac {1}{13}}{x^{13}}\) | \(60\) |
gosper | \(-\frac {78 x^{11}+572 x^{10}+2145 x^{9}+5148 x^{8}+8580 x^{7}+10296 x^{6}+9009 x^{5}+5720 x^{4}+2574 x^{3}+780 x^{2}+143 x +12}{156 x^{13}}\) | \(61\) |
default | \(-\frac {5}{x^{11}}-\frac {33}{x^{5}}-\frac {110}{3 x^{9}}-\frac {55}{4 x^{4}}-\frac {11}{12 x^{12}}-\frac {55}{x^{6}}-\frac {1}{13 x^{13}}-\frac {1}{2 x^{2}}-\frac {231}{4 x^{8}}-\frac {66}{x^{7}}-\frac {33}{2 x^{10}}-\frac {11}{3 x^{3}}\) | \(62\) |
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. 60 vs.
\(2 (21) = 42\).
time = 0.28, size = 60, normalized size = 2.40 \begin {gather*} -\frac {78 \, x^{11} + 572 \, x^{10} + 2145 \, x^{9} + 5148 \, x^{8} + 8580 \, x^{7} + 10296 \, x^{6} + 9009 \, x^{5} + 5720 \, x^{4} + 2574 \, x^{3} + 780 \, x^{2} + 143 \, x + 12}{156 \, 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. 60 vs.
\(2 (21) = 42\).
time = 2.89, size = 60, normalized size = 2.40 \begin {gather*} -\frac {78 \, x^{11} + 572 \, x^{10} + 2145 \, x^{9} + 5148 \, x^{8} + 8580 \, x^{7} + 10296 \, x^{6} + 9009 \, x^{5} + 5720 \, x^{4} + 2574 \, x^{3} + 780 \, x^{2} + 143 \, x + 12}{156 \, 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. 61 vs.
\(2 (19) = 38\).
time = 0.07, size = 61, normalized size = 2.44 \begin {gather*} \frac {- 78 x^{11} - 572 x^{10} - 2145 x^{9} - 5148 x^{8} - 8580 x^{7} - 10296 x^{6} - 9009 x^{5} - 5720 x^{4} - 2574 x^{3} - 780 x^{2} - 143 x - 12}{156 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. 60 vs.
\(2 (21) = 42\).
time = 0.61, size = 60, normalized size = 2.40 \begin {gather*} -\frac {78 \, x^{11} + 572 \, x^{10} + 2145 \, x^{9} + 5148 \, x^{8} + 8580 \, x^{7} + 10296 \, x^{6} + 9009 \, x^{5} + 5720 \, x^{4} + 2574 \, x^{3} + 780 \, x^{2} + 143 \, x + 12}{156 \, x^{13}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 60, normalized size = 2.40 \begin {gather*} -\frac {\frac {x^{11}}{2}+\frac {11\,x^{10}}{3}+\frac {55\,x^9}{4}+33\,x^8+55\,x^7+66\,x^6+\frac {231\,x^5}{4}+\frac {110\,x^4}{3}+\frac {33\,x^3}{2}+5\,x^2+\frac {11\,x}{12}+\frac {1}{13}}{x^{13}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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