Integrand size = 17, antiderivative size = 14 \[ \int \frac {1}{3} (-64-30 x+(-8-4 x) \log (x)) \, dx=\frac {2}{3} (-4-x) x (7+\log (x)) \]
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Leaf count is larger than twice the leaf count of optimal. \(36\) vs. \(2(14)=28\).
Time = 0.01 (sec) , antiderivative size = 36, normalized size of antiderivative = 2.57, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {12, 2350, 9} \[ \int \frac {1}{3} (-64-30 x+(-8-4 x) \log (x)) \, dx=-5 x^2-\frac {2}{3} x^2 \log (x)-\frac {64 x}{3}+\frac {1}{3} (x+4)^2-\frac {8}{3} x \log (x) \]
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Rule 9
Rule 12
Rule 2350
Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} \int (-64-30 x+(-8-4 x) \log (x)) \, dx \\ & = -\frac {64 x}{3}-5 x^2+\frac {1}{3} \int (-8-4 x) \log (x) \, dx \\ & = -\frac {64 x}{3}-5 x^2-\frac {8}{3} x \log (x)-\frac {2}{3} x^2 \log (x)-\frac {1}{3} \int 2 (-4-x) \, dx \\ & = -\frac {64 x}{3}-5 x^2+\frac {1}{3} (4+x)^2-\frac {8}{3} x \log (x)-\frac {2}{3} x^2 \log (x) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(29\) vs. \(2(14)=28\).
Time = 0.01 (sec) , antiderivative size = 29, normalized size of antiderivative = 2.07 \[ \int \frac {1}{3} (-64-30 x+(-8-4 x) \log (x)) \, dx=-\frac {56 x}{3}-\frac {14 x^2}{3}-\frac {8}{3} x \log (x)-\frac {2}{3} x^2 \log (x) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(21\) vs. \(2(10)=20\).
Time = 0.02 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.57
method | result | size |
default | \(-\frac {56 x}{3}-\frac {2 x^{2} \ln \left (x \right )}{3}-\frac {14 x^{2}}{3}-\frac {8 x \ln \left (x \right )}{3}\) | \(22\) |
norman | \(-\frac {56 x}{3}-\frac {2 x^{2} \ln \left (x \right )}{3}-\frac {14 x^{2}}{3}-\frac {8 x \ln \left (x \right )}{3}\) | \(22\) |
parallelrisch | \(-\frac {56 x}{3}-\frac {2 x^{2} \ln \left (x \right )}{3}-\frac {14 x^{2}}{3}-\frac {8 x \ln \left (x \right )}{3}\) | \(22\) |
parts | \(-\frac {56 x}{3}-\frac {2 x^{2} \ln \left (x \right )}{3}-\frac {14 x^{2}}{3}-\frac {8 x \ln \left (x \right )}{3}\) | \(22\) |
risch | \(\frac {\left (-2 x^{2}-8 x \right ) \ln \left (x \right )}{3}-\frac {14 x^{2}}{3}-\frac {56 x}{3}\) | \(23\) |
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Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.43 \[ \int \frac {1}{3} (-64-30 x+(-8-4 x) \log (x)) \, dx=-\frac {14}{3} \, x^{2} - \frac {2}{3} \, {\left (x^{2} + 4 \, x\right )} \log \left (x\right ) - \frac {56}{3} \, x \]
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Time = 0.05 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.93 \[ \int \frac {1}{3} (-64-30 x+(-8-4 x) \log (x)) \, dx=- \frac {14 x^{2}}{3} - \frac {56 x}{3} + \left (- \frac {2 x^{2}}{3} - \frac {8 x}{3}\right ) \log {\left (x \right )} \]
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Time = 0.18 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.43 \[ \int \frac {1}{3} (-64-30 x+(-8-4 x) \log (x)) \, dx=-\frac {14}{3} \, x^{2} - \frac {2}{3} \, {\left (x^{2} + 4 \, x\right )} \log \left (x\right ) - \frac {56}{3} \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 21 vs. \(2 (10) = 20\).
Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.50 \[ \int \frac {1}{3} (-64-30 x+(-8-4 x) \log (x)) \, dx=-\frac {2}{3} \, x^{2} \log \left (x\right ) - \frac {14}{3} \, x^{2} - \frac {8}{3} \, x \log \left (x\right ) - \frac {56}{3} \, x \]
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Time = 7.90 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{3} (-64-30 x+(-8-4 x) \log (x)) \, dx=-\frac {2\,x\,\left (\ln \left (x\right )+7\right )\,\left (x+4\right )}{3} \]
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