Integrand size = 39, antiderivative size = 17 \[ \int \frac {-320+82 x+16 x^2-3 x^3+\left (128-52 x+8 x^2\right ) \log (x)-4 x \log ^2(x)}{x} \, dx=(16-x) \left (9+(5+x-2 \log (x))^2\right ) \]
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Leaf count is larger than twice the leaf count of optimal. \(43\) vs. \(2(17)=34\).
Time = 0.04 (sec) , antiderivative size = 43, normalized size of antiderivative = 2.53, number of steps used = 11, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {14, 2404, 2332, 2338, 2341, 2333} \[ \int \frac {-320+82 x+16 x^2-3 x^3+\left (128-52 x+8 x^2\right ) \log (x)-4 x \log ^2(x)}{x} \, dx=-x^3+6 x^2+4 x^2 \log (x)+126 x-4 x \log ^2(x)+64 \log ^2(x)-44 x \log (x)-320 \log (x) \]
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Rule 14
Rule 2332
Rule 2333
Rule 2338
Rule 2341
Rule 2404
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {-320+82 x+16 x^2-3 x^3}{x}+\frac {4 \left (32-13 x+2 x^2\right ) \log (x)}{x}-4 \log ^2(x)\right ) \, dx \\ & = 4 \int \frac {\left (32-13 x+2 x^2\right ) \log (x)}{x} \, dx-4 \int \log ^2(x) \, dx+\int \frac {-320+82 x+16 x^2-3 x^3}{x} \, dx \\ & = -4 x \log ^2(x)+4 \int \left (-13 \log (x)+\frac {32 \log (x)}{x}+2 x \log (x)\right ) \, dx+8 \int \log (x) \, dx+\int \left (82-\frac {320}{x}+16 x-3 x^2\right ) \, dx \\ & = 74 x+8 x^2-x^3-320 \log (x)+8 x \log (x)-4 x \log ^2(x)+8 \int x \log (x) \, dx-52 \int \log (x) \, dx+128 \int \frac {\log (x)}{x} \, dx \\ & = 126 x+6 x^2-x^3-320 \log (x)-44 x \log (x)+4 x^2 \log (x)+64 \log ^2(x)-4 x \log ^2(x) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(43\) vs. \(2(17)=34\).
Time = 0.02 (sec) , antiderivative size = 43, normalized size of antiderivative = 2.53 \[ \int \frac {-320+82 x+16 x^2-3 x^3+\left (128-52 x+8 x^2\right ) \log (x)-4 x \log ^2(x)}{x} \, dx=126 x+6 x^2-x^3-320 \log (x)-44 x \log (x)+4 x^2 \log (x)+64 \log ^2(x)-4 x \log ^2(x) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(40\) vs. \(2(17)=34\).
Time = 0.02 (sec) , antiderivative size = 41, normalized size of antiderivative = 2.41
method | result | size |
risch | \(\left (-4 x +64\right ) \ln \left (x \right )^{2}+\left (4 x^{2}-44 x \right ) \ln \left (x \right )-x^{3}+6 x^{2}+126 x -320 \ln \left (x \right )\) | \(41\) |
default | \(-4 x \ln \left (x \right )^{2}-44 x \ln \left (x \right )+126 x +4 x^{2} \ln \left (x \right )+6 x^{2}-x^{3}+64 \ln \left (x \right )^{2}-320 \ln \left (x \right )\) | \(44\) |
norman | \(-4 x \ln \left (x \right )^{2}-44 x \ln \left (x \right )+126 x +4 x^{2} \ln \left (x \right )+6 x^{2}-x^{3}+64 \ln \left (x \right )^{2}-320 \ln \left (x \right )\) | \(44\) |
parallelrisch | \(-4 x \ln \left (x \right )^{2}-44 x \ln \left (x \right )+126 x +4 x^{2} \ln \left (x \right )+6 x^{2}-x^{3}+64 \ln \left (x \right )^{2}-320 \ln \left (x \right )\) | \(44\) |
parts | \(-4 x \ln \left (x \right )^{2}-44 x \ln \left (x \right )+126 x +4 x^{2} \ln \left (x \right )+6 x^{2}-x^{3}+64 \ln \left (x \right )^{2}-320 \ln \left (x \right )\) | \(44\) |
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Leaf count of result is larger than twice the leaf count of optimal. 35 vs. \(2 (16) = 32\).
Time = 0.25 (sec) , antiderivative size = 35, normalized size of antiderivative = 2.06 \[ \int \frac {-320+82 x+16 x^2-3 x^3+\left (128-52 x+8 x^2\right ) \log (x)-4 x \log ^2(x)}{x} \, dx=-x^{3} - 4 \, {\left (x - 16\right )} \log \left (x\right )^{2} + 6 \, x^{2} + 4 \, {\left (x^{2} - 11 \, x - 80\right )} \log \left (x\right ) + 126 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 37 vs. \(2 (14) = 28\).
Time = 0.07 (sec) , antiderivative size = 37, normalized size of antiderivative = 2.18 \[ \int \frac {-320+82 x+16 x^2-3 x^3+\left (128-52 x+8 x^2\right ) \log (x)-4 x \log ^2(x)}{x} \, dx=- x^{3} + 6 x^{2} + 126 x + \left (64 - 4 x\right ) \log {\left (x \right )}^{2} + \left (4 x^{2} - 44 x\right ) \log {\left (x \right )} - 320 \log {\left (x \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (16) = 32\).
Time = 0.20 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.88 \[ \int \frac {-320+82 x+16 x^2-3 x^3+\left (128-52 x+8 x^2\right ) \log (x)-4 x \log ^2(x)}{x} \, dx=-x^{3} + 4 \, x^{2} \log \left (x\right ) - 4 \, {\left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 2\right )} x + 6 \, x^{2} - 52 \, x \log \left (x\right ) + 64 \, \log \left (x\right )^{2} + 134 \, x - 320 \, \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 38 vs. \(2 (16) = 32\).
Time = 0.28 (sec) , antiderivative size = 38, normalized size of antiderivative = 2.24 \[ \int \frac {-320+82 x+16 x^2-3 x^3+\left (128-52 x+8 x^2\right ) \log (x)-4 x \log ^2(x)}{x} \, dx=-x^{3} - 4 \, {\left (x - 16\right )} \log \left (x\right )^{2} + 6 \, x^{2} + 4 \, {\left (x^{2} - 11 \, x\right )} \log \left (x\right ) + 126 \, x - 320 \, \log \left (x\right ) \]
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Time = 8.57 (sec) , antiderivative size = 43, normalized size of antiderivative = 2.53 \[ \int \frac {-320+82 x+16 x^2-3 x^3+\left (128-52 x+8 x^2\right ) \log (x)-4 x \log ^2(x)}{x} \, dx=-x^3+4\,x^2\,\ln \left (x\right )+6\,x^2-4\,x\,{\ln \left (x\right )}^2-44\,x\,\ln \left (x\right )+126\,x+64\,{\ln \left (x\right )}^2-320\,\ln \left (x\right ) \]
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