Integrand size = 15, antiderivative size = 21 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-x+\frac {x}{e^4}-4 x^2-(5+x)^2 \]
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Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12} \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=\frac {x}{e^4}-\frac {1}{20} (10 x+11)^2 \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {\int \left (1+e^4 (-11-10 x)\right ) \, dx}{e^4} \\ & = \frac {x}{e^4}-\frac {1}{20} (11+10 x)^2 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-11 x+\frac {x}{e^4}-5 x^2 \]
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Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67
method | result | size |
risch | \(-5 x^{2}-11 x +x \,{\mathrm e}^{-4}\) | \(14\) |
gosper | \(-x \left (5 x \,{\mathrm e}^{4}+11 \,{\mathrm e}^{4}-1\right ) {\mathrm e}^{-4}\) | \(19\) |
default | \({\mathrm e}^{-4} \left (-5 x^{2} {\mathrm e}^{4}-11 x \,{\mathrm e}^{4}+x \right )\) | \(20\) |
norman | \(-5 x^{2}-{\mathrm e}^{-4} \left (11 \,{\mathrm e}^{4}-1\right ) x\) | \(20\) |
parallelrisch | \({\mathrm e}^{-4} \left ({\mathrm e}^{4} \left (-5 x^{2}-11 x \right )+x \right )\) | \(20\) |
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Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-{\left ({\left (5 \, x^{2} + 11 \, x\right )} e^{4} - x\right )} e^{\left (-4\right )} \]
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Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=- 5 x^{2} + \frac {x \left (1 - 11 e^{4}\right )}{e^{4}} \]
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Time = 0.17 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-{\left ({\left (5 \, x^{2} + 11 \, x\right )} e^{4} - x\right )} e^{\left (-4\right )} \]
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Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-{\left ({\left (5 \, x^{2} + 11 \, x\right )} e^{4} - x\right )} e^{\left (-4\right )} \]
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Time = 8.39 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.76 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-\frac {{\mathrm {e}}^{-8}\,{\left ({\mathrm {e}}^4\,\left (10\,x+11\right )-1\right )}^2}{20} \]
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