Optimal. Leaf size=22 \[ x^2+\log \left (x+x^4 \left (x+9 \left (3+x^2\right )\right )^4\right ) \]
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Rubi [B] time = 0.61, antiderivative size = 54, normalized size of antiderivative = 2.45, number of steps used = 3, number of rules used = 2, integrand size = 112, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {2074, 1587} \begin {gather*} x^2+\log \left (6561 x^{11}+2916 x^{10}+79218 x^9+26280 x^8+357211 x^7+78840 x^6+712962 x^5+78732 x^4+531441 x^3+1\right )+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1}{x}+2 x+\frac {x^2 \left (27+x+9 x^2\right )^3 \left (81+7 x+99 x^2\right )}{1+531441 x^3+78732 x^4+712962 x^5+78840 x^6+357211 x^7+26280 x^8+79218 x^9+2916 x^{10}+6561 x^{11}}\right ) \, dx\\ &=x^2+\log (x)+\int \frac {x^2 \left (27+x+9 x^2\right )^3 \left (81+7 x+99 x^2\right )}{1+531441 x^3+78732 x^4+712962 x^5+78840 x^6+357211 x^7+26280 x^8+79218 x^9+2916 x^{10}+6561 x^{11}} \, dx\\ &=x^2+\log (x)+\log \left (1+531441 x^3+78732 x^4+712962 x^5+78840 x^6+357211 x^7+26280 x^8+79218 x^9+2916 x^{10}+6561 x^{11}\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.03, size = 54, normalized size = 2.45 \begin {gather*} x^2+\log (x)+\log \left (1+531441 x^3+78732 x^4+712962 x^5+78840 x^6+357211 x^7+26280 x^8+79218 x^9+2916 x^{10}+6561 x^{11}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.69, size = 52, normalized size = 2.36 \begin {gather*} x^{2} + \log \left (6561 \, x^{12} + 2916 \, x^{11} + 79218 \, x^{10} + 26280 \, x^{9} + 357211 \, x^{8} + 78840 \, x^{7} + 712962 \, x^{6} + 78732 \, x^{5} + 531441 \, x^{4} + x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.35, size = 56, normalized size = 2.55 \begin {gather*} x^{2} + \log \left ({\left | 6561 \, x^{11} + 2916 \, x^{10} + 79218 \, x^{9} + 26280 \, x^{8} + 357211 \, x^{7} + 78840 \, x^{6} + 712962 \, x^{5} + 78732 \, x^{4} + 531441 \, x^{3} + 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 53, normalized size = 2.41
method | result | size |
risch | \(x^{2}+\ln \left (6561 x^{12}+2916 x^{11}+79218 x^{10}+26280 x^{9}+357211 x^{8}+78840 x^{7}+712962 x^{6}+78732 x^{5}+531441 x^{4}+x \right )\) | \(53\) |
default | \(x^{2}+\ln \relax (x )+\ln \left (6561 x^{11}+2916 x^{10}+79218 x^{9}+26280 x^{8}+357211 x^{7}+78840 x^{6}+712962 x^{5}+78732 x^{4}+531441 x^{3}+1\right )\) | \(55\) |
norman | \(x^{2}+\ln \relax (x )+\ln \left (6561 x^{11}+2916 x^{10}+79218 x^{9}+26280 x^{8}+357211 x^{7}+78840 x^{6}+712962 x^{5}+78732 x^{4}+531441 x^{3}+1\right )\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.38, size = 54, normalized size = 2.45 \begin {gather*} x^{2} + \log \left (6561 \, x^{11} + 2916 \, x^{10} + 79218 \, x^{9} + 26280 \, x^{8} + 357211 \, x^{7} + 78840 \, x^{6} + 712962 \, x^{5} + 78732 \, x^{4} + 531441 \, x^{3} + 1\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.70, size = 52, normalized size = 2.36 \begin {gather*} \ln \left (6561\,x^{12}+2916\,x^{11}+79218\,x^{10}+26280\,x^9+357211\,x^8+78840\,x^7+712962\,x^6+78732\,x^5+531441\,x^4+x\right )+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.17, size = 51, normalized size = 2.32 \begin {gather*} x^{2} + \log {\left (6561 x^{12} + 2916 x^{11} + 79218 x^{10} + 26280 x^{9} + 357211 x^{8} + 78840 x^{7} + 712962 x^{6} + 78732 x^{5} + 531441 x^{4} + x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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