Integrand size = 20, antiderivative size = 12 \[ \int \frac {5 x+e^{7+x} x (5+5 x)}{x} \, dx=5 \left (2+x+e^{7+x} x\right ) \]
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Time = 0.01 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.75, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {14, 2207, 2225} \[ \int \frac {5 x+e^{7+x} x (5+5 x)}{x} \, dx=5 x-5 e^{x+7}+5 e^{x+7} (x+1) \]
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Rule 14
Rule 2207
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \int \left (5+5 e^{7+x} (1+x)\right ) \, dx \\ & = 5 x+5 \int e^{7+x} (1+x) \, dx \\ & = 5 x+5 e^{7+x} (1+x)-5 \int e^{7+x} \, dx \\ & = -5 e^{7+x}+5 x+5 e^{7+x} (1+x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {5 x+e^{7+x} x (5+5 x)}{x} \, dx=5 x+5 e^{7+x} x \]
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Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00
method | result | size |
risch | \(5 x +5 x \,{\mathrm e}^{x +7}\) | \(12\) |
default | \(5 x +5 \,{\mathrm e}^{\ln \left (x \right )+x +7}\) | \(13\) |
norman | \(5 x +5 \,{\mathrm e}^{\ln \left (x \right )+x +7}\) | \(13\) |
parallelrisch | \(5 x +5 \,{\mathrm e}^{\ln \left (x \right )+x +7}\) | \(13\) |
parts | \(5 x +5 \,{\mathrm e}^{\ln \left (x \right )+x +7}\) | \(13\) |
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none
Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {5 x+e^{7+x} x (5+5 x)}{x} \, dx=5 \, x + 5 \, e^{\left (x + \log \left (x\right ) + 7\right )} \]
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Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {5 x+e^{7+x} x (5+5 x)}{x} \, dx=5 x e^{x + 7} + 5 x \]
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none
Time = 0.19 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.92 \[ \int \frac {5 x+e^{7+x} x (5+5 x)}{x} \, dx=5 \, {\left (x e^{7} - e^{7}\right )} e^{x} + 5 \, x + 5 \, e^{\left (x + 7\right )} \]
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none
Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92 \[ \int \frac {5 x+e^{7+x} x (5+5 x)}{x} \, dx=5 \, x e^{\left (x + 7\right )} + 5 \, x \]
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Time = 11.11 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {5 x+e^{7+x} x (5+5 x)}{x} \, dx=5\,x\,\left ({\mathrm {e}}^{x+7}+1\right ) \]
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