Integrand size = 22, antiderivative size = 25 \[ \int \frac {64+e^{\frac {x^4}{256}} x^4}{32 x} \, dx=\log \left (\frac {e^{2 e^{\frac {x^4}{256}}} x^2}{3 \log (4)}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.64, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {12, 14, 2240} \[ \int \frac {64+e^{\frac {x^4}{256}} x^4}{32 x} \, dx=2 e^{\frac {x^4}{256}}+2 \log (x) \]
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Rule 12
Rule 14
Rule 2240
Rubi steps \begin{align*} \text {integral}& = \frac {1}{32} \int \frac {64+e^{\frac {x^4}{256}} x^4}{x} \, dx \\ & = \frac {1}{32} \int \left (\frac {64}{x}+e^{\frac {x^4}{256}} x^3\right ) \, dx \\ & = 2 \log (x)+\frac {1}{32} \int e^{\frac {x^4}{256}} x^3 \, dx \\ & = 2 e^{\frac {x^4}{256}}+2 \log (x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.64 \[ \int \frac {64+e^{\frac {x^4}{256}} x^4}{32 x} \, dx=2 e^{\frac {x^4}{256}}+2 \log (x) \]
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Time = 0.10 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.56
method | result | size |
default | \(2 \,{\mathrm e}^{\frac {x^{4}}{256}}+2 \ln \left (x \right )\) | \(14\) |
norman | \(2 \,{\mathrm e}^{\frac {x^{4}}{256}}+2 \ln \left (x \right )\) | \(14\) |
risch | \(2 \,{\mathrm e}^{\frac {x^{4}}{256}}+2 \ln \left (x \right )\) | \(14\) |
parallelrisch | \(2 \,{\mathrm e}^{\frac {x^{4}}{256}}+2 \ln \left (x \right )\) | \(14\) |
parts | \(2 \,{\mathrm e}^{\frac {x^{4}}{256}}+2 \ln \left (x \right )\) | \(14\) |
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Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.52 \[ \int \frac {64+e^{\frac {x^4}{256}} x^4}{32 x} \, dx=2 \, e^{\left (\frac {1}{256} \, x^{4}\right )} + 2 \, \log \left (x\right ) \]
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Time = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.48 \[ \int \frac {64+e^{\frac {x^4}{256}} x^4}{32 x} \, dx=2 e^{\frac {x^{4}}{256}} + 2 \log {\left (x \right )} \]
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Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.52 \[ \int \frac {64+e^{\frac {x^4}{256}} x^4}{32 x} \, dx=2 \, e^{\left (\frac {1}{256} \, x^{4}\right )} + 2 \, \log \left (x\right ) \]
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Time = 0.25 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.68 \[ \int \frac {64+e^{\frac {x^4}{256}} x^4}{32 x} \, dx=2 \, e^{\left (\frac {1}{256} \, x^{4}\right )} + \frac {1}{2} \, \log \left (\frac {1}{256} \, x^{4}\right ) \]
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Time = 9.38 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.52 \[ \int \frac {64+e^{\frac {x^4}{256}} x^4}{32 x} \, dx=2\,{\mathrm {e}}^{\frac {x^4}{256}}+2\,\ln \left (x\right ) \]
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