Integrand size = 32, antiderivative size = 29 \[ \int \frac {63-3 e^9-66 x+9 x^2-3 \log ^2(16)}{e^9+\log ^2(16)} \, dx=3 \left (5-x+\frac {\left (-4+(-5+x)^2-x\right ) x}{e^9+\log ^2(16)}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.97, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {12} \[ \int \frac {63-3 e^9-66 x+9 x^2-3 \log ^2(16)}{e^9+\log ^2(16)} \, dx=\frac {3 x^3}{e^9+\log ^2(16)}-\frac {33 x^2}{e^9+\log ^2(16)}+\frac {3 x \left (21-e^9-\log ^2(16)\right )}{e^9+\log ^2(16)} \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {\int \left (63-3 e^9-66 x+9 x^2-3 \log ^2(16)\right ) \, dx}{e^9+\log ^2(16)} \\ & = -\frac {33 x^2}{e^9+\log ^2(16)}+\frac {3 x^3}{e^9+\log ^2(16)}+\frac {3 x \left (21-e^9-\log ^2(16)\right )}{e^9+\log ^2(16)} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.28 \[ \int \frac {63-3 e^9-66 x+9 x^2-3 \log ^2(16)}{e^9+\log ^2(16)} \, dx=-\frac {3 \left (-21 x+e^9 x+11 x^2-x^3+x \log ^2(16)\right )}{e^9+\log ^2(16)} \]
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Time = 0.05 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.14
method | result | size |
gosper | \(-\frac {3 x \left (16 \ln \left (2\right )^{2}-x^{2}+{\mathrm e}^{9}+11 x -21\right )}{16 \ln \left (2\right )^{2}+{\mathrm e}^{9}}\) | \(33\) |
default | \(\frac {-48 x \ln \left (2\right )^{2}+3 x^{3}-3 x \,{\mathrm e}^{9}-33 x^{2}+63 x}{16 \ln \left (2\right )^{2}+{\mathrm e}^{9}}\) | \(38\) |
parallelrisch | \(\frac {3 x^{3}-33 x^{2}+\left (-48 \ln \left (2\right )^{2}-3 \,{\mathrm e}^{9}+63\right ) x}{16 \ln \left (2\right )^{2}+{\mathrm e}^{9}}\) | \(38\) |
norman | \(-\frac {33 x^{2}}{16 \ln \left (2\right )^{2}+{\mathrm e}^{9}}+\frac {3 x^{3}}{16 \ln \left (2\right )^{2}+{\mathrm e}^{9}}-\frac {3 \left (16 \ln \left (2\right )^{2}+{\mathrm e}^{9}-21\right ) x}{16 \ln \left (2\right )^{2}+{\mathrm e}^{9}}\) | \(58\) |
risch | \(-\frac {48 x \ln \left (2\right )^{2}}{16 \ln \left (2\right )^{2}+{\mathrm e}^{9}}+\frac {3 x^{3}}{16 \ln \left (2\right )^{2}+{\mathrm e}^{9}}-\frac {3 x \,{\mathrm e}^{9}}{16 \ln \left (2\right )^{2}+{\mathrm e}^{9}}-\frac {33 x^{2}}{16 \ln \left (2\right )^{2}+{\mathrm e}^{9}}+\frac {63 x}{16 \ln \left (2\right )^{2}+{\mathrm e}^{9}}\) | \(82\) |
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Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.28 \[ \int \frac {63-3 e^9-66 x+9 x^2-3 \log ^2(16)}{e^9+\log ^2(16)} \, dx=\frac {3 \, {\left (x^{3} - 16 \, x \log \left (2\right )^{2} - 11 \, x^{2} - x e^{9} + 21 \, x\right )}}{16 \, \log \left (2\right )^{2} + e^{9}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (26) = 52\).
Time = 0.03 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.86 \[ \int \frac {63-3 e^9-66 x+9 x^2-3 \log ^2(16)}{e^9+\log ^2(16)} \, dx=\frac {3 x^{3}}{16 \log {\left (2 \right )}^{2} + e^{9}} - \frac {33 x^{2}}{16 \log {\left (2 \right )}^{2} + e^{9}} + \frac {x \left (- 3 e^{9} - 48 \log {\left (2 \right )}^{2} + 63\right )}{16 \log {\left (2 \right )}^{2} + e^{9}} \]
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Time = 0.20 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.28 \[ \int \frac {63-3 e^9-66 x+9 x^2-3 \log ^2(16)}{e^9+\log ^2(16)} \, dx=\frac {3 \, {\left (x^{3} - 16 \, x \log \left (2\right )^{2} - 11 \, x^{2} - x e^{9} + 21 \, x\right )}}{16 \, \log \left (2\right )^{2} + e^{9}} \]
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Time = 0.26 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.28 \[ \int \frac {63-3 e^9-66 x+9 x^2-3 \log ^2(16)}{e^9+\log ^2(16)} \, dx=\frac {3 \, {\left (x^{3} - 16 \, x \log \left (2\right )^{2} - 11 \, x^{2} - x e^{9} + 21 \, x\right )}}{16 \, \log \left (2\right )^{2} + e^{9}} \]
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Time = 11.42 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.10 \[ \int \frac {63-3 e^9-66 x+9 x^2-3 \log ^2(16)}{e^9+\log ^2(16)} \, dx=-\frac {3\,x\,\left (-x^2+11\,x+{\mathrm {e}}^9+16\,{\ln \left (2\right )}^2-21\right )}{{\mathrm {e}}^9+16\,{\ln \left (2\right )}^2} \]
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