Integrand size = 23, antiderivative size = 16 \[ \int \frac {-15 x^3+e x \left (-20+3 x^2\right )}{e x^7} \, dx=\frac {-1+\frac {5}{e}+\frac {4}{x^2}}{x^3} \]
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Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {12, 14} \[ \int \frac {-15 x^3+e x \left (-20+3 x^2\right )}{e x^7} \, dx=\frac {4}{x^5}+\frac {5-e}{e x^3} \]
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Rule 12
Rule 14
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {-15 x^3+e x \left (-20+3 x^2\right )}{x^7} \, dx}{e} \\ & = \frac {\int \left (-\frac {20 e}{x^6}+\frac {3 (-5+e)}{x^4}\right ) \, dx}{e} \\ & = \frac {4}{x^5}+\frac {5-e}{e x^3} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {-15 x^3+e x \left (-20+3 x^2\right )}{e x^7} \, dx=\frac {4}{x^5}+\frac {5-e}{e x^3} \]
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Time = 0.08 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.38
method | result | size |
norman | \(\frac {4 x -\left ({\mathrm e}-5\right ) {\mathrm e}^{-1} x^{3}}{x^{6}}\) | \(22\) |
risch | \(\frac {{\mathrm e}^{-1} \left (\left (5-{\mathrm e}\right ) x^{2}+4 \,{\mathrm e}\right )}{x^{5}}\) | \(22\) |
default | \(\frac {4}{x^{5}}-\frac {1}{x^{3}}+\frac {5 \,{\mathrm e}^{-1}}{x^{3}}\) | \(24\) |
parts | \(\frac {4}{x^{5}}-\frac {1}{x^{3}}+\frac {5 \,{\mathrm e}^{-1}}{x^{3}}\) | \(24\) |
parallelrisch | \(\frac {\left (5 x^{5}-{\mathrm e}^{\ln \left (x \right )+1} x^{4}+4 x^{2} {\mathrm e}^{\ln \left (x \right )+1}\right ) {\mathrm e}^{-1}}{x^{8}}\) | \(38\) |
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Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.31 \[ \int \frac {-15 x^3+e x \left (-20+3 x^2\right )}{e x^7} \, dx=\frac {{\left (5 \, x^{2} - {\left (x^{2} - 4\right )} e\right )} e^{\left (-1\right )}}{x^{5}} \]
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Time = 0.11 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {-15 x^3+e x \left (-20+3 x^2\right )}{e x^7} \, dx=- \frac {x^{2} \left (-5 + e\right ) - 4 e}{e x^{5}} \]
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Time = 0.18 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {-15 x^3+e x \left (-20+3 x^2\right )}{e x^7} \, dx=-\frac {{\left (x^{2} {\left (e - 5\right )} - 4 \, e\right )} e^{\left (-1\right )}}{x^{5}} \]
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Time = 0.28 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.44 \[ \int \frac {-15 x^3+e x \left (-20+3 x^2\right )}{e x^7} \, dx=-\frac {{\left (x^{2} e - 5 \, x^{2} - 4 \, e\right )} e^{\left (-1\right )}}{x^{5}} \]
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Time = 7.49 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {-15 x^3+e x \left (-20+3 x^2\right )}{e x^7} \, dx=\frac {\left (5\,{\mathrm {e}}^{-1}-1\right )\,x^2+4}{x^5} \]
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