Integrand size = 13, antiderivative size = 10 \[ \int \left (56 x+8 e x+16 x^3\right ) \, dx=\left (7+e+2 x^2\right )^2 \]
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Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.40, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {6} \[ \int \left (56 x+8 e x+16 x^3\right ) \, dx=4 x^4+4 (7+e) x^2 \]
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Rule 6
Rubi steps \begin{align*} \text {integral}& = \int \left ((56+8 e) x+16 x^3\right ) \, dx \\ & = 4 (7+e) x^2+4 x^4 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.70 \[ \int \left (56 x+8 e x+16 x^3\right ) \, dx=28 x^2+4 e x^2+4 x^4 \]
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Time = 0.20 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20
method | result | size |
default | \(\left (2 x^{2}+7+{\mathrm e}\right )^{2}\) | \(12\) |
gosper | \(4 x^{2} \left (x^{2}+{\mathrm e}+7\right )\) | \(13\) |
norman | \(\left (4 \,{\mathrm e}+28\right ) x^{2}+4 x^{4}\) | \(17\) |
risch | \(4 x^{2} {\mathrm e}+4 x^{4}+28 x^{2}\) | \(19\) |
parallelrisch | \(4 x^{2} {\mathrm e}+4 x^{4}+28 x^{2}\) | \(19\) |
parts | \(4 x^{2} {\mathrm e}+4 x^{4}+28 x^{2}\) | \(19\) |
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none
Time = 0.22 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.80 \[ \int \left (56 x+8 e x+16 x^3\right ) \, dx=4 \, x^{4} + 4 \, x^{2} e + 28 \, x^{2} \]
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Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.40 \[ \int \left (56 x+8 e x+16 x^3\right ) \, dx=4 x^{4} + x^{2} \cdot \left (4 e + 28\right ) \]
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none
Time = 0.20 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.80 \[ \int \left (56 x+8 e x+16 x^3\right ) \, dx=4 \, x^{4} + 4 \, x^{2} e + 28 \, x^{2} \]
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none
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.80 \[ \int \left (56 x+8 e x+16 x^3\right ) \, dx=4 \, x^{4} + 4 \, x^{2} e + 28 \, x^{2} \]
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Time = 9.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.60 \[ \int \left (56 x+8 e x+16 x^3\right ) \, dx=4\,x^4+\left (4\,\mathrm {e}+28\right )\,x^2 \]
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