Integrand size = 13, antiderivative size = 20 \[ \int (180+110 x+(30+20 x) \log (x)) \, dx=4 \left (-e^3+\frac {5}{2} x (3+x) (5+\log (x))\right ) \]
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Time = 0.01 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.40, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {2350, 9} \[ \int (180+110 x+(30+20 x) \log (x)) \, dx=55 x^2+10 x^2 \log (x)+180 x-5 (x+3)^2+30 x \log (x) \]
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Rule 9
Rule 2350
Rubi steps \begin{align*} \text {integral}& = 180 x+55 x^2+\int (30+20 x) \log (x) \, dx \\ & = 180 x+55 x^2+30 x \log (x)+10 x^2 \log (x)-\int 10 (3+x) \, dx \\ & = 180 x+55 x^2-5 (3+x)^2+30 x \log (x)+10 x^2 \log (x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int (180+110 x+(30+20 x) \log (x)) \, dx=150 x+50 x^2+30 x \log (x)+10 x^2 \log (x) \]
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Time = 0.03 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10
method | result | size |
default | \(150 x +10 x^{2} \ln \left (x \right )+50 x^{2}+30 x \ln \left (x \right )\) | \(22\) |
norman | \(150 x +10 x^{2} \ln \left (x \right )+50 x^{2}+30 x \ln \left (x \right )\) | \(22\) |
risch | \(\left (10 x^{2}+30 x \right ) \ln \left (x \right )+50 x^{2}+150 x\) | \(22\) |
parallelrisch | \(150 x +10 x^{2} \ln \left (x \right )+50 x^{2}+30 x \ln \left (x \right )\) | \(22\) |
parts | \(150 x +10 x^{2} \ln \left (x \right )+50 x^{2}+30 x \ln \left (x \right )\) | \(22\) |
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none
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int (180+110 x+(30+20 x) \log (x)) \, dx=50 \, x^{2} + 10 \, {\left (x^{2} + 3 \, x\right )} \log \left (x\right ) + 150 \, x \]
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Time = 0.04 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int (180+110 x+(30+20 x) \log (x)) \, dx=50 x^{2} + 150 x + \left (10 x^{2} + 30 x\right ) \log {\left (x \right )} \]
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none
Time = 0.18 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int (180+110 x+(30+20 x) \log (x)) \, dx=50 \, x^{2} + 10 \, {\left (x^{2} + 3 \, x\right )} \log \left (x\right ) + 150 \, x \]
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none
Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int (180+110 x+(30+20 x) \log (x)) \, dx=10 \, x^{2} \log \left (x\right ) + 50 \, x^{2} + 30 \, x \log \left (x\right ) + 150 \, x \]
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Time = 8.69 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.50 \[ \int (180+110 x+(30+20 x) \log (x)) \, dx=10\,x\,\left (\ln \left (x\right )+5\right )\,\left (x+3\right ) \]
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