Integrand size = 112, antiderivative size = 22 \[ \int \frac {1+2 x^2+2125764 x^3+393660 x^4+5340654 x^5+709344 x^6+4283612 x^7+394200 x^8+1506602 x^9+84636 x^{10}+237168 x^{11}+5832 x^{12}+13122 x^{13}}{x+531441 x^4+78732 x^5+712962 x^6+78840 x^7+357211 x^8+26280 x^9+79218 x^{10}+2916 x^{11}+6561 x^{12}} \, dx=x^2+\log \left (x+x^4 \left (x+9 \left (3+x^2\right )\right )^4\right ) \]
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Leaf count is larger than twice the leaf count of optimal. \(54\) vs. \(2(22)=44\).
Time = 0.37 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.45, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {2099, 1601} \[ \int \frac {1+2 x^2+2125764 x^3+393660 x^4+5340654 x^5+709344 x^6+4283612 x^7+394200 x^8+1506602 x^9+84636 x^{10}+237168 x^{11}+5832 x^{12}+13122 x^{13}}{x+531441 x^4+78732 x^5+712962 x^6+78840 x^7+357211 x^8+26280 x^9+79218 x^{10}+2916 x^{11}+6561 x^{12}} \, dx=x^2+\log \left (6561 x^{11}+2916 x^{10}+79218 x^9+26280 x^8+357211 x^7+78840 x^6+712962 x^5+78732 x^4+531441 x^3+1\right )+\log (x) \]
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Rule 1601
Rule 2099
Rubi steps \begin{align*} \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{align*}
Leaf count is larger than twice the leaf count of optimal. \(54\) vs. \(2(22)=44\).
Time = 0.06 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.45 \[ \int \frac {1+2 x^2+2125764 x^3+393660 x^4+5340654 x^5+709344 x^6+4283612 x^7+394200 x^8+1506602 x^9+84636 x^{10}+237168 x^{11}+5832 x^{12}+13122 x^{13}}{x+531441 x^4+78732 x^5+712962 x^6+78840 x^7+357211 x^8+26280 x^9+79218 x^{10}+2916 x^{11}+6561 x^{12}} \, dx=x^2+\log (x)+\log \left (1+531441 x^3+78732 x^4+712962 x^5+78840 x^6+357211 x^7+26280 x^8+79218 x^9+2916 x^{10}+6561 x^{11}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(52\) vs. \(2(21)=42\).
Time = 0.04 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.41
method | result | size |
risch | \(x^{2}+\ln \left (6561 x^{12}+2916 x^{11}+79218 x^{10}+26280 x^{9}+357211 x^{8}+78840 x^{7}+712962 x^{6}+78732 x^{5}+531441 x^{4}+x \right )\) | \(53\) |
parallelrisch | \(x^{2}+\ln \left (x \right )+\ln \left (x^{11}+\frac {4}{9} x^{10}+\frac {326}{27} x^{9}+\frac {2920}{729} x^{8}+\frac {357211}{6561} x^{7}+\frac {2920}{243} x^{6}+\frac {326}{3} x^{5}+12 x^{4}+81 x^{3}+\frac {1}{6561}\right )\) | \(53\) |
default | \(x^{2}+\ln \left (x \right )+\ln \left (6561 x^{11}+2916 x^{10}+79218 x^{9}+26280 x^{8}+357211 x^{7}+78840 x^{6}+712962 x^{5}+78732 x^{4}+531441 x^{3}+1\right )\) | \(55\) |
norman | \(x^{2}+\ln \left (x \right )+\ln \left (6561 x^{11}+2916 x^{10}+79218 x^{9}+26280 x^{8}+357211 x^{7}+78840 x^{6}+712962 x^{5}+78732 x^{4}+531441 x^{3}+1\right )\) | \(55\) |
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Leaf count of result is larger than twice the leaf count of optimal. 52 vs. \(2 (21) = 42\).
Time = 0.27 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.36 \[ \int \frac {1+2 x^2+2125764 x^3+393660 x^4+5340654 x^5+709344 x^6+4283612 x^7+394200 x^8+1506602 x^9+84636 x^{10}+237168 x^{11}+5832 x^{12}+13122 x^{13}}{x+531441 x^4+78732 x^5+712962 x^6+78840 x^7+357211 x^8+26280 x^9+79218 x^{10}+2916 x^{11}+6561 x^{12}} \, dx=x^{2} + \log \left (6561 \, x^{12} + 2916 \, x^{11} + 79218 \, x^{10} + 26280 \, x^{9} + 357211 \, x^{8} + 78840 \, x^{7} + 712962 \, x^{6} + 78732 \, x^{5} + 531441 \, x^{4} + x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (19) = 38\).
Time = 0.08 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.32 \[ \int \frac {1+2 x^2+2125764 x^3+393660 x^4+5340654 x^5+709344 x^6+4283612 x^7+394200 x^8+1506602 x^9+84636 x^{10}+237168 x^{11}+5832 x^{12}+13122 x^{13}}{x+531441 x^4+78732 x^5+712962 x^6+78840 x^7+357211 x^8+26280 x^9+79218 x^{10}+2916 x^{11}+6561 x^{12}} \, dx=x^{2} + \log {\left (6561 x^{12} + 2916 x^{11} + 79218 x^{10} + 26280 x^{9} + 357211 x^{8} + 78840 x^{7} + 712962 x^{6} + 78732 x^{5} + 531441 x^{4} + x \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (21) = 42\).
Time = 0.18 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.45 \[ \int \frac {1+2 x^2+2125764 x^3+393660 x^4+5340654 x^5+709344 x^6+4283612 x^7+394200 x^8+1506602 x^9+84636 x^{10}+237168 x^{11}+5832 x^{12}+13122 x^{13}}{x+531441 x^4+78732 x^5+712962 x^6+78840 x^7+357211 x^8+26280 x^9+79218 x^{10}+2916 x^{11}+6561 x^{12}} \, dx=x^{2} + \log \left (6561 \, x^{11} + 2916 \, x^{10} + 79218 \, x^{9} + 26280 \, x^{8} + 357211 \, x^{7} + 78840 \, x^{6} + 712962 \, x^{5} + 78732 \, x^{4} + 531441 \, x^{3} + 1\right ) + \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (21) = 42\).
Time = 0.30 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.55 \[ \int \frac {1+2 x^2+2125764 x^3+393660 x^4+5340654 x^5+709344 x^6+4283612 x^7+394200 x^8+1506602 x^9+84636 x^{10}+237168 x^{11}+5832 x^{12}+13122 x^{13}}{x+531441 x^4+78732 x^5+712962 x^6+78840 x^7+357211 x^8+26280 x^9+79218 x^{10}+2916 x^{11}+6561 x^{12}} \, dx=x^{2} + \log \left ({\left | 6561 \, x^{11} + 2916 \, x^{10} + 79218 \, x^{9} + 26280 \, x^{8} + 357211 \, x^{7} + 78840 \, x^{6} + 712962 \, x^{5} + 78732 \, x^{4} + 531441 \, x^{3} + 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \]
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Time = 8.61 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.36 \[ \int \frac {1+2 x^2+2125764 x^3+393660 x^4+5340654 x^5+709344 x^6+4283612 x^7+394200 x^8+1506602 x^9+84636 x^{10}+237168 x^{11}+5832 x^{12}+13122 x^{13}}{x+531441 x^4+78732 x^5+712962 x^6+78840 x^7+357211 x^8+26280 x^9+79218 x^{10}+2916 x^{11}+6561 x^{12}} \, dx=\ln \left (6561\,x^{12}+2916\,x^{11}+79218\,x^{10}+26280\,x^9+357211\,x^8+78840\,x^7+712962\,x^6+78732\,x^5+531441\,x^4+x\right )+x^2 \]
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