Optimal. Leaf size=9 \[ \frac {1}{12} (x+1)^{12} \]
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Rubi [A] time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {27, 32} \begin {gather*} \frac {1}{12} (x+1)^{12} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 32
Rubi steps
\begin {align*} \int (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int (1+x)^{11} \, dx\\ &=\frac {1}{12} (1+x)^{12}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {1}{12} (x+1)^{12} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1+x) \left (1+2 x+x^2\right )^5 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.36, size = 55, normalized size = 6.11 \begin {gather*} \frac {1}{12} x^{12} + x^{11} + \frac {11}{2} x^{10} + \frac {55}{3} x^{9} + \frac {165}{4} x^{8} + 66 x^{7} + 77 x^{6} + 66 x^{5} + \frac {165}{4} x^{4} + \frac {55}{3} x^{3} + \frac {11}{2} x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 62, normalized size = 6.89 \begin {gather*} \frac {1}{12} \, {\left (x^{2} + 2 \, x\right )}^{6} + \frac {1}{2} \, {\left (x^{2} + 2 \, x\right )}^{5} + \frac {5}{4} \, {\left (x^{2} + 2 \, x\right )}^{4} + \frac {5}{3} \, {\left (x^{2} + 2 \, x\right )}^{3} + \frac {5}{4} \, {\left (x^{2} + 2 \, x\right )}^{2} + \frac {1}{2} \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 56, normalized size = 6.22 \begin {gather*} \frac {1}{12} x^{12}+x^{11}+\frac {11}{2} x^{10}+\frac {55}{3} x^{9}+\frac {165}{4} x^{8}+66 x^{7}+77 x^{6}+66 x^{5}+\frac {165}{4} x^{4}+\frac {55}{3} x^{3}+\frac {11}{2} x^{2}+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 12, normalized size = 1.33 \begin {gather*} \frac {1}{12} \, {\left (x^{2} + 2 \, x + 1\right )}^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 55, normalized size = 6.11 \begin {gather*} \frac {x^{12}}{12}+x^{11}+\frac {11\,x^{10}}{2}+\frac {55\,x^9}{3}+\frac {165\,x^8}{4}+66\,x^7+77\,x^6+66\,x^5+\frac {165\,x^4}{4}+\frac {55\,x^3}{3}+\frac {11\,x^2}{2}+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 65, normalized size = 7.22 \begin {gather*} \frac {x^{12}}{12} + x^{11} + \frac {11 x^{10}}{2} + \frac {55 x^{9}}{3} + \frac {165 x^{8}}{4} + 66 x^{7} + 77 x^{6} + 66 x^{5} + \frac {165 x^{4}}{4} + \frac {55 x^{3}}{3} + \frac {11 x^{2}}{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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