Integrand size = 27, antiderivative size = 27 \[ \int \frac {4+2 e^8 x^3 \left (i \pi +\log \left (\frac {59}{16}\right )\right )}{e^8 x^2} \, dx=-\frac {\frac {4}{e^8}+x}{x}+x^2 \left (i \pi +\log \left (\frac {59}{16}\right )\right ) \]
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Time = 0.01 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {12, 14} \[ \int \frac {4+2 e^8 x^3 \left (i \pi +\log \left (\frac {59}{16}\right )\right )}{e^8 x^2} \, dx=-\frac {4}{e^8 x}+x^2 \left (\log \left (\frac {59}{16}\right )+i \pi \right ) \]
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Rule 12
Rule 14
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {4+2 e^8 x^3 \left (i \pi +\log \left (\frac {59}{16}\right )\right )}{x^2} \, dx}{e^8} \\ & = \frac {\int \left (\frac {4}{x^2}+2 e^8 x \left (i \pi +\log \left (\frac {59}{16}\right )\right )\right ) \, dx}{e^8} \\ & = -\frac {4}{e^8 x}+x^2 \left (i \pi +\log \left (\frac {59}{16}\right )\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85 \[ \int \frac {4+2 e^8 x^3 \left (i \pi +\log \left (\frac {59}{16}\right )\right )}{e^8 x^2} \, dx=-\frac {4}{e^8 x}+x^2 \left (i \pi +\log \left (\frac {59}{16}\right )\right ) \]
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Time = 0.15 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00
method | result | size |
default | \(2 \,{\mathrm e}^{-8} \left (\frac {{\mathrm e}^{8} \left (\ln \left (\frac {59}{16}\right )+i \pi \right ) x^{2}}{2}-\frac {2}{x}\right )\) | \(27\) |
risch | \(-4 x^{2} \ln \left (2\right )+\ln \left (59\right ) x^{2}+i \pi \,x^{2}-\frac {4 \,{\mathrm e}^{-8}}{x}\) | \(29\) |
parallelrisch | \(\frac {{\mathrm e}^{-8} \left (i \pi \,x^{3} {\mathrm e}^{8}+\ln \left (\frac {59}{16}\right ) x^{3} {\mathrm e}^{8}-4\right )}{x}\) | \(32\) |
norman | \(\frac {\left ({\mathrm e}^{4} \left (\ln \left (59\right )-4 \ln \left (2\right )+i \pi \right ) x^{3}-4 \,{\mathrm e}^{-4}\right ) {\mathrm e}^{-4}}{x}\) | \(33\) |
gosper | \(\frac {\left (-i \ln \left (\frac {59}{16}\right ) x^{3} {\mathrm e}^{8}+\pi \,x^{3} {\mathrm e}^{8}+4 i\right ) \left (i \pi \,x^{3} {\mathrm e}^{8}+\ln \left (\frac {59}{16}\right ) x^{3} {\mathrm e}^{8}+2\right ) {\mathrm e}^{-8}}{x \left (-i \ln \left (\frac {59}{16}\right ) x^{3} {\mathrm e}^{8}+\pi \,x^{3} {\mathrm e}^{8}-2 i\right )}\) | \(82\) |
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Time = 0.24 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89 \[ \int \frac {4+2 e^8 x^3 \left (i \pi +\log \left (\frac {59}{16}\right )\right )}{e^8 x^2} \, dx=\frac {{\left (i \, \pi x^{3} e^{8} + x^{3} e^{8} \log \left (\frac {59}{16}\right ) - 4\right )} e^{\left (-8\right )}}{x} \]
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Time = 0.05 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {4+2 e^8 x^3 \left (i \pi +\log \left (\frac {59}{16}\right )\right )}{e^8 x^2} \, dx=\frac {x^{2} \left (- 4 e^{8} \log {\left (2 \right )} + e^{8} \log {\left (59 \right )} + i \pi e^{8}\right ) - \frac {4}{x}}{e^{8}} \]
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Time = 0.18 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.96 \[ \int \frac {4+2 e^8 x^3 \left (i \pi +\log \left (\frac {59}{16}\right )\right )}{e^8 x^2} \, dx=-{\left ({\left (-i \, \pi e^{8} - e^{8} \log \left (\frac {59}{16}\right )\right )} x^{2} + \frac {4}{x}\right )} e^{\left (-8\right )} \]
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Time = 0.28 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {4+2 e^8 x^3 \left (i \pi +\log \left (\frac {59}{16}\right )\right )}{e^8 x^2} \, dx=-{\left (-i \, \pi x^{2} e^{8} - x^{2} e^{8} \log \left (\frac {59}{16}\right ) + \frac {4}{x}\right )} e^{\left (-8\right )} \]
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Time = 0.11 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.70 \[ \int \frac {4+2 e^8 x^3 \left (i \pi +\log \left (\frac {59}{16}\right )\right )}{e^8 x^2} \, dx=-\frac {4\,{\mathrm {e}}^{-8}}{x}+x^2\,\left (\ln \left (\frac {59}{16}\right )+\Pi \,1{}\mathrm {i}\right ) \]
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