Integrand size = 28, antiderivative size = 26 \[ \int \frac {12 x^4+24 x^5-4 e x^5+4 \log (2)}{3 x^2} \, dx=-1+\frac {1}{3} (4+x-(-5+e) x) \left (x^3-\frac {\log (2)}{x}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {6, 12, 14} \[ \int \frac {12 x^4+24 x^5-4 e x^5+4 \log (2)}{3 x^2} \, dx=\frac {1}{3} (6-e) x^4+\frac {4 x^3}{3}-\frac {\log (16)}{3 x} \]
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Rule 6
Rule 12
Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \frac {12 x^4+(24-4 e) x^5+4 \log (2)}{3 x^2} \, dx \\ & = \frac {1}{3} \int \frac {12 x^4+(24-4 e) x^5+4 \log (2)}{x^2} \, dx \\ & = \frac {1}{3} \int \left (12 x^2-4 (-6+e) x^3+\frac {\log (16)}{x^2}\right ) \, dx \\ & = \frac {4 x^3}{3}+\frac {1}{3} (6-e) x^4-\frac {\log (16)}{3 x} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.04 \[ \int \frac {12 x^4+24 x^5-4 e x^5+4 \log (2)}{3 x^2} \, dx=\frac {4}{3} \left (x^3+\frac {1}{4} (6-e) x^4-\frac {\log (2)}{x}\right ) \]
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Time = 0.09 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.96
method | result | size |
norman | \(\frac {\left (-\frac {{\mathrm e}}{3}+2\right ) x^{5}+\frac {4 x^{4}}{3}-\frac {4 \ln \left (2\right )}{3}}{x}\) | \(25\) |
default | \(-\frac {x^{4} {\mathrm e}}{3}+2 x^{4}+\frac {4 x^{3}}{3}-\frac {4 \ln \left (2\right )}{3 x}\) | \(26\) |
risch | \(-\frac {x^{4} {\mathrm e}}{3}+2 x^{4}+\frac {4 x^{3}}{3}-\frac {4 \ln \left (2\right )}{3 x}\) | \(26\) |
gosper | \(-\frac {x^{5} {\mathrm e}-6 x^{5}-4 x^{4}+4 \ln \left (2\right )}{3 x}\) | \(27\) |
parallelrisch | \(-\frac {x^{5} {\mathrm e}-6 x^{5}-4 x^{4}+4 \ln \left (2\right )}{3 x}\) | \(27\) |
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Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {12 x^4+24 x^5-4 e x^5+4 \log (2)}{3 x^2} \, dx=-\frac {x^{5} e - 6 \, x^{5} - 4 \, x^{4} + 4 \, \log \left (2\right )}{3 \, x} \]
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Time = 0.05 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int \frac {12 x^4+24 x^5-4 e x^5+4 \log (2)}{3 x^2} \, dx=\frac {x^{4} \cdot \left (6 - e\right )}{3} + \frac {4 x^{3}}{3} - \frac {4 \log {\left (2 \right )}}{3 x} \]
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Time = 0.17 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.85 \[ \int \frac {12 x^4+24 x^5-4 e x^5+4 \log (2)}{3 x^2} \, dx=-\frac {1}{3} \, x^{4} {\left (e - 6\right )} + \frac {4}{3} \, x^{3} - \frac {4 \, \log \left (2\right )}{3 \, x} \]
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Time = 0.26 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.96 \[ \int \frac {12 x^4+24 x^5-4 e x^5+4 \log (2)}{3 x^2} \, dx=-\frac {1}{3} \, x^{4} e + 2 \, x^{4} + \frac {4}{3} \, x^{3} - \frac {4 \, \log \left (2\right )}{3 \, x} \]
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Time = 12.07 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int \frac {12 x^4+24 x^5-4 e x^5+4 \log (2)}{3 x^2} \, dx=\frac {4\,x^3}{3}-\frac {4\,\ln \left (2\right )}{3\,x}-x^4\,\left (\frac {\mathrm {e}}{3}-2\right ) \]
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