Optimal. Leaf size=19 \[ \frac {1}{1+\frac {1}{(-5+x)^5}+\frac {1}{(-3+x)^3}+\frac {1}{-1+x}} \]
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Rubi [A]
time = 0.04, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6818}
\begin {gather*} \frac {1}{\frac {1}{(x-3)^3}+\frac {1}{(x-5)^5}+\frac {1}{x-1}+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\frac {1}{1+\frac {1}{(-5+x)^5}+\frac {1}{(-3+x)^3}+\frac {1}{-1+x}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 19, normalized size = 1.00 \begin {gather*} \frac {1}{1+\frac {1}{(-5+x)^5}+\frac {1}{(-3+x)^3}+\frac {1}{-1+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. \(86\) vs.
\(2(19)=38\).
time = 0.12, size = 87, normalized size = 4.58
method | result | size |
gosper | \(-\frac {x^{8}-34 x^{7}+503 x^{6}-4228 x^{5}+22076 x^{4}-73260 x^{3}+150661 x^{2}-175054 x +87527}{x^{9}-34 x^{8}+502 x^{7}-4201 x^{6}+21774 x^{5}-71474 x^{4}+144740 x^{3}-164339 x^{2}+78071 x +3152}\) | \(86\) |
default | \(\frac {-x^{8}+34 x^{7}-503 x^{6}+4228 x^{5}-22076 x^{4}+73260 x^{3}-150661 x^{2}+175054 x -87527}{x^{9}-34 x^{8}+502 x^{7}-4201 x^{6}+21774 x^{5}-71474 x^{4}+144740 x^{3}-164339 x^{2}+78071 x +3152}\) | \(87\) |
risch | \(\frac {-x^{8}+34 x^{7}-503 x^{6}+4228 x^{5}-22076 x^{4}+73260 x^{3}-150661 x^{2}+175054 x -87527}{x^{9}-34 x^{8}+502 x^{7}-4201 x^{6}+21774 x^{5}-71474 x^{4}+144740 x^{3}-164339 x^{2}+78071 x +3152}\) | \(87\) |
parallelrisch | \(\frac {-x^{8}+34 x^{7}-503 x^{6}+4228 x^{5}-22076 x^{4}+73260 x^{3}-150661 x^{2}+175054 x -87527}{x^{9}-34 x^{8}+502 x^{7}-4201 x^{6}+21774 x^{5}-71474 x^{4}+144740 x^{3}-164339 x^{2}+78071 x +3152}\) | \(87\) |
norman | \(\frac {-x^{17}+69 x^{16}-2229 x^{15}+44761 x^{14}-625602 x^{13}+6455858 x^{12}-50913715 x^{11}+313280159 x^{10}-1521750430 x^{9}+5864557678 x^{8}-17915907435 x^{7}+43095090791 x^{6}-80517901754 x^{5}+114214737850 x^{4}-118540274125 x^{3}+84593570625 x^{2}-36925453125 x +7385090625}{\left (x -1\right ) \left (-3+x \right )^{3} \left (x -5\right )^{5} \left (x^{9}-34 x^{8}+502 x^{7}-4201 x^{6}+21774 x^{5}-71474 x^{4}+144740 x^{3}-164339 x^{2}+78071 x +3152\right )}\) | \(147\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 19, normalized size = 1.00 \begin {gather*} \frac {1}{\frac {1}{x - 1} + \frac {1}{{\left (x - 3\right )}^{3}} + \frac {1}{{\left (x - 5\right )}^{5}} + 1} \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. 85 vs.
\(2 (19) = 38\).
time = 0.57, size = 85, normalized size = 4.47 \begin {gather*} -\frac {x^{8} - 34 \, x^{7} + 503 \, x^{6} - 4228 \, x^{5} + 22076 \, x^{4} - 73260 \, x^{3} + 150661 \, x^{2} - 175054 \, x + 87527}{x^{9} - 34 \, x^{8} + 502 \, x^{7} - 4201 \, x^{6} + 21774 \, x^{5} - 71474 \, x^{4} + 144740 \, x^{3} - 164339 \, x^{2} + 78071 \, x + 3152} \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. 82 vs.
\(2 (20) = 40\).
time = 0.50, size = 82, normalized size = 4.32 \begin {gather*} \frac {- x^{8} + 34 x^{7} - 503 x^{6} + 4228 x^{5} - 22076 x^{4} + 73260 x^{3} - 150661 x^{2} + 175054 x - 87527}{x^{9} - 34 x^{8} + 502 x^{7} - 4201 x^{6} + 21774 x^{5} - 71474 x^{4} + 144740 x^{3} - 164339 x^{2} + 78071 x + 3152} \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. 85 vs.
\(2 (19) = 38\).
time = 0.48, size = 85, normalized size = 4.47 \begin {gather*} -\frac {x^{8} - 34 \, x^{7} + 503 \, x^{6} - 4228 \, x^{5} + 22076 \, x^{4} - 73260 \, x^{3} + 150661 \, x^{2} - 175054 \, x + 87527}{x^{9} - 34 \, x^{8} + 502 \, x^{7} - 4201 \, x^{6} + 21774 \, x^{5} - 71474 \, x^{4} + 144740 \, x^{3} - 164339 \, x^{2} + 78071 \, x + 3152} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.31, size = 85, normalized size = 4.47 \begin {gather*} -\frac {x^8-34\,x^7+503\,x^6-4228\,x^5+22076\,x^4-73260\,x^3+150661\,x^2-175054\,x+87527}{x^9-34\,x^8+502\,x^7-4201\,x^6+21774\,x^5-71474\,x^4+144740\,x^3-164339\,x^2+78071\,x+3152} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {not solved} \end {gather*}
Warning: Unable to verify antiderivative.
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