Integrand size = 19, antiderivative size = 16 \[ \int \frac {-1-x-4 e^{1024-4 x} x}{x} \, dx=4+e^{1024-4 x}-x-\log (x) \]
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Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {14, 2225, 45} \[ \int \frac {-1-x-4 e^{1024-4 x} x}{x} \, dx=-x+e^{1024-4 x}-\log (x) \]
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Rule 14
Rule 45
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \int \left (-4 e^{1024-4 x}+\frac {-1-x}{x}\right ) \, dx \\ & = -\left (4 \int e^{1024-4 x} \, dx\right )+\int \frac {-1-x}{x} \, dx \\ & = e^{1024-4 x}+\int \left (-1-\frac {1}{x}\right ) \, dx \\ & = e^{1024-4 x}-x-\log (x) \\ \end{align*}
Time = 0.09 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {-1-x-4 e^{1024-4 x} x}{x} \, dx=e^{1024-4 x}-x-\log (x) \]
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Time = 0.10 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94
method | result | size |
risch | \({\mathrm e}^{1024-4 x}-x -\ln \left (x \right )\) | \(15\) |
norman | \({\mathrm e}^{1024-4 x}-x -\ln \left (x \right )\) | \(17\) |
parallelrisch | \({\mathrm e}^{1024-4 x}-x -\ln \left (x \right )\) | \(17\) |
parts | \({\mathrm e}^{1024-4 x}-x -\ln \left (x \right )\) | \(17\) |
derivativedivides | \(256-x +256 \ln \left (-x \right )-257 \ln \left (x \right )+{\mathrm e}^{1024-4 x}\) | \(24\) |
default | \(256-x +256 \ln \left (-x \right )-257 \ln \left (x \right )+{\mathrm e}^{1024-4 x}\) | \(24\) |
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Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {-1-x-4 e^{1024-4 x} x}{x} \, dx=-x + e^{\left (-4 \, x + 1024\right )} - \log \left (x\right ) \]
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Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int \frac {-1-x-4 e^{1024-4 x} x}{x} \, dx=- x + e^{1024 - 4 x} - \log {\left (x \right )} \]
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Time = 0.18 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {-1-x-4 e^{1024-4 x} x}{x} \, dx=-x + e^{\left (-4 \, x + 1024\right )} - \log \left (x\right ) \]
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Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {-1-x-4 e^{1024-4 x} x}{x} \, dx=-x + e^{\left (-4 \, x + 1024\right )} - \log \left (x\right ) \]
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Time = 14.71 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {-1-x-4 e^{1024-4 x} x}{x} \, dx={\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^{1024}-\ln \left (x\right )-x \]
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