Optimal. Leaf size=19 \[ -\frac {1}{12} (1+x)^{12}+\frac {1}{13} (1+x)^{13} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {27, 45}
\begin {gather*} \frac {1}{13} (x+1)^{13}-\frac {1}{12} (x+1)^{12} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 45
Rubi steps
\begin {align*} \int x (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int x (1+x)^{11} \, dx\\ &=\int \left (-(1+x)^{11}+(1+x)^{12}\right ) \, dx\\ &=-\frac {1}{12} (1+x)^{12}+\frac {1}{13} (1+x)^{13}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(19)=38\).
time = 0.00, size = 77, normalized size = 4.05 \begin {gather*} \frac {x^2}{2}+\frac {11 x^3}{3}+\frac {55 x^4}{4}+33 x^5+55 x^6+66 x^7+\frac {231 x^8}{4}+\frac {110 x^9}{3}+\frac {33 x^{10}}{2}+5 x^{11}+\frac {11 x^{12}}{12}+\frac {x^{13}}{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. \(61\) vs.
\(2(15)=30\).
time = 0.65, size = 62, normalized size = 3.26
method | result | size |
gosper | \(\frac {x^{2} \left (12 x^{11}+143 x^{10}+780 x^{9}+2574 x^{8}+5720 x^{7}+9009 x^{6}+10296 x^{5}+8580 x^{4}+5148 x^{3}+2145 x^{2}+572 x +78\right )}{156}\) | \(61\) |
default | \(\frac {1}{13} x^{13}+\frac {11}{12} x^{12}+5 x^{11}+\frac {33}{2} x^{10}+\frac {110}{3} x^{9}+\frac {231}{4} x^{8}+66 x^{7}+55 x^{6}+33 x^{5}+\frac {55}{4} x^{4}+\frac {11}{3} x^{3}+\frac {1}{2} x^{2}\) | \(62\) |
norman | \(\frac {1}{13} x^{13}+\frac {11}{12} x^{12}+5 x^{11}+\frac {33}{2} x^{10}+\frac {110}{3} x^{9}+\frac {231}{4} x^{8}+66 x^{7}+55 x^{6}+33 x^{5}+\frac {55}{4} x^{4}+\frac {11}{3} x^{3}+\frac {1}{2} x^{2}\) | \(62\) |
risch | \(\frac {1}{13} x^{13}+\frac {11}{12} x^{12}+5 x^{11}+\frac {33}{2} x^{10}+\frac {110}{3} x^{9}+\frac {231}{4} x^{8}+66 x^{7}+55 x^{6}+33 x^{5}+\frac {55}{4} x^{4}+\frac {11}{3} x^{3}+\frac {1}{2} x^{2}\) | \(62\) |
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. 61 vs.
\(2 (15) = 30\).
time = 0.28, size = 61, normalized size = 3.21 \begin {gather*} \frac {1}{13} \, x^{13} + \frac {11}{12} \, x^{12} + 5 \, x^{11} + \frac {33}{2} \, x^{10} + \frac {110}{3} \, x^{9} + \frac {231}{4} \, x^{8} + 66 \, x^{7} + 55 \, x^{6} + 33 \, x^{5} + \frac {55}{4} \, x^{4} + \frac {11}{3} \, x^{3} + \frac {1}{2} \, x^{2} \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. 61 vs.
\(2 (15) = 30\).
time = 2.37, size = 61, normalized size = 3.21 \begin {gather*} \frac {1}{13} \, x^{13} + \frac {11}{12} \, x^{12} + 5 \, x^{11} + \frac {33}{2} \, x^{10} + \frac {110}{3} \, x^{9} + \frac {231}{4} \, x^{8} + 66 \, x^{7} + 55 \, x^{6} + 33 \, x^{5} + \frac {55}{4} \, x^{4} + \frac {11}{3} \, x^{3} + \frac {1}{2} \, x^{2} \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. 70 vs.
\(2 (12) = 24\).
time = 0.01, size = 70, normalized size = 3.68 \begin {gather*} \frac {x^{13}}{13} + \frac {11 x^{12}}{12} + 5 x^{11} + \frac {33 x^{10}}{2} + \frac {110 x^{9}}{3} + \frac {231 x^{8}}{4} + 66 x^{7} + 55 x^{6} + 33 x^{5} + \frac {55 x^{4}}{4} + \frac {11 x^{3}}{3} + \frac {x^{2}}{2} \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. 61 vs.
\(2 (15) = 30\).
time = 1.28, size = 61, normalized size = 3.21 \begin {gather*} \frac {1}{13} \, x^{13} + \frac {11}{12} \, x^{12} + 5 \, x^{11} + \frac {33}{2} \, x^{10} + \frac {110}{3} \, x^{9} + \frac {231}{4} \, x^{8} + 66 \, x^{7} + 55 \, x^{6} + 33 \, x^{5} + \frac {55}{4} \, x^{4} + \frac {11}{3} \, x^{3} + \frac {1}{2} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 61, normalized size = 3.21 \begin {gather*} \frac {x^{13}}{13}+\frac {11\,x^{12}}{12}+5\,x^{11}+\frac {33\,x^{10}}{2}+\frac {110\,x^9}{3}+\frac {231\,x^8}{4}+66\,x^7+55\,x^6+33\,x^5+\frac {55\,x^4}{4}+\frac {11\,x^3}{3}+\frac {x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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