Integrand size = 9, antiderivative size = 8 \[ \int \left (36 x+9 x^2\right ) \, dx=3 x^2 (6+x) \]
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Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.38, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (36 x+9 x^2\right ) \, dx=3 x^3+18 x^2 \]
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Rubi steps \begin{align*} \text {integral}& = 18 x^2+3 x^3 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.38 \[ \int \left (36 x+9 x^2\right ) \, dx=18 x^2+3 x^3 \]
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Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.12
method | result | size |
gosper | \(3 x^{2} \left (6+x \right )\) | \(9\) |
default | \(3 x^{3}+18 x^{2}\) | \(12\) |
norman | \(3 x^{3}+18 x^{2}\) | \(12\) |
risch | \(3 x^{3}+18 x^{2}\) | \(12\) |
parallelrisch | \(3 x^{3}+18 x^{2}\) | \(12\) |
parts | \(3 x^{3}+18 x^{2}\) | \(12\) |
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none
Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.38 \[ \int \left (36 x+9 x^2\right ) \, dx=3 \, x^{3} + 18 \, x^{2} \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \left (36 x+9 x^2\right ) \, dx=3 x^{3} + 18 x^{2} \]
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none
Time = 0.18 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.38 \[ \int \left (36 x+9 x^2\right ) \, dx=3 \, x^{3} + 18 \, x^{2} \]
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none
Time = 0.25 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.38 \[ \int \left (36 x+9 x^2\right ) \, dx=3 \, x^{3} + 18 \, x^{2} \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \left (36 x+9 x^2\right ) \, dx=3\,x^2\,\left (x+6\right ) \]
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