Integrand size = 18, antiderivative size = 18 \[ \int \frac {1}{4} \left (-267+510 x+e^3 (-4+170 x)\right ) \, dx=\left (-1+\frac {85 x}{4}\right ) \left (-3+3 x+e^3 x\right ) \]
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Time = 0.00 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.50, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {12} \[ \int \frac {1}{4} \left (-267+510 x+e^3 (-4+170 x)\right ) \, dx=\frac {255 x^2}{4}+\frac {1}{340} e^3 (2-85 x)^2-\frac {267 x}{4} \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {1}{4} \int \left (-267+510 x+e^3 (-4+170 x)\right ) \, dx \\ & = \frac {1}{340} e^3 (2-85 x)^2-\frac {267 x}{4}+\frac {255 x^2}{4} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.50 \[ \int \frac {1}{4} \left (-267+510 x+e^3 (-4+170 x)\right ) \, dx=\frac {1}{4} \left (-267 x-4 e^3 x+255 x^2+85 e^3 x^2\right ) \]
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Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
method | result | size |
gosper | \(\frac {x \left (85 x \,{\mathrm e}^{3}-4 \,{\mathrm e}^{3}+255 x -267\right )}{4}\) | \(18\) |
norman | \(\left (-{\mathrm e}^{3}-\frac {267}{4}\right ) x +\left (\frac {85 \,{\mathrm e}^{3}}{4}+\frac {255}{4}\right ) x^{2}\) | \(20\) |
default | \(\frac {85 x^{2} {\mathrm e}^{3}}{4}-x \,{\mathrm e}^{3}+\frac {255 x^{2}}{4}-\frac {267 x}{4}\) | \(22\) |
risch | \(\frac {85 x^{2} {\mathrm e}^{3}}{4}-x \,{\mathrm e}^{3}+\frac {255 x^{2}}{4}-\frac {267 x}{4}\) | \(22\) |
parallelrisch | \(\frac {85 x^{2} {\mathrm e}^{3}}{4}-x \,{\mathrm e}^{3}+\frac {255 x^{2}}{4}-\frac {267 x}{4}\) | \(22\) |
parts | \(\frac {85 x^{2} {\mathrm e}^{3}}{4}-x \,{\mathrm e}^{3}+\frac {255 x^{2}}{4}-\frac {267 x}{4}\) | \(22\) |
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Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {1}{4} \left (-267+510 x+e^3 (-4+170 x)\right ) \, dx=\frac {255}{4} \, x^{2} + \frac {1}{4} \, {\left (85 \, x^{2} - 4 \, x\right )} e^{3} - \frac {267}{4} \, x \]
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Time = 0.02 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {1}{4} \left (-267+510 x+e^3 (-4+170 x)\right ) \, dx=x^{2} \cdot \left (\frac {255}{4} + \frac {85 e^{3}}{4}\right ) + x \left (- \frac {267}{4} - e^{3}\right ) \]
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none
Time = 0.19 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {1}{4} \left (-267+510 x+e^3 (-4+170 x)\right ) \, dx=\frac {255}{4} \, x^{2} + \frac {1}{4} \, {\left (85 \, x^{2} - 4 \, x\right )} e^{3} - \frac {267}{4} \, x \]
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none
Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {1}{4} \left (-267+510 x+e^3 (-4+170 x)\right ) \, dx=\frac {255}{4} \, x^{2} + \frac {1}{4} \, {\left (85 \, x^{2} - 4 \, x\right )} e^{3} - \frac {267}{4} \, x \]
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Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {1}{4} \left (-267+510 x+e^3 (-4+170 x)\right ) \, dx=x^2\,\left (\frac {85\,{\mathrm {e}}^3}{4}+\frac {255}{4}\right )-x\,\left ({\mathrm {e}}^3+\frac {267}{4}\right ) \]
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