Optimal. Leaf size=30 \[ \frac {3 x}{5}+\frac {(-5+x) \left (1+e^5+\frac {3+x}{5 x^2}\right )^2}{x^2} \]
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Rubi [B] time = 0.07, antiderivative size = 78, normalized size of antiderivative = 2.60, number of steps used = 3, number of rules used = 2, integrand size = 77, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {12, 14} \begin {gather*} -\frac {9}{5 x^6}-\frac {21}{25 x^5}-\frac {149+150 e^5}{25 x^4}-\frac {19+20 e^5}{25 x^3}-\frac {23+48 e^5+25 e^{10}}{5 x^2}+\frac {3 x}{5}+\frac {\left (1+e^5\right )^2}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \frac {270+105 x+596 x^2+57 x^3+230 x^4-25 x^5+15 x^7+e^5 \left (600 x^2+60 x^3+480 x^4-50 x^5\right )+e^{10} \left (250 x^4-25 x^5\right )}{x^7} \, dx\\ &=\frac {1}{25} \int \left (15+\frac {270}{x^7}+\frac {105}{x^6}+\frac {4 \left (149+150 e^5\right )}{x^5}+\frac {3 \left (19+20 e^5\right )}{x^4}+\frac {10 \left (23+48 e^5+25 e^{10}\right )}{x^3}-\frac {25 \left (1+e^5\right )^2}{x^2}\right ) \, dx\\ &=-\frac {9}{5 x^6}-\frac {21}{25 x^5}-\frac {149+150 e^5}{25 x^4}-\frac {19+20 e^5}{25 x^3}-\frac {23+48 e^5+25 e^{10}}{5 x^2}+\frac {\left (1+e^5\right )^2}{x}+\frac {3 x}{5}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.03, size = 69, normalized size = 2.30 \begin {gather*} \frac {1}{25} \left (-\frac {45}{x^6}-\frac {21}{x^5}+\frac {-149-150 e^5}{x^4}+\frac {-19-20 e^5}{x^3}-\frac {5 \left (23+48 e^5+25 e^{10}\right )}{x^2}+\frac {25 \left (1+e^5\right )^2}{x}+15 x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.55, size = 73, normalized size = 2.43 \begin {gather*} \frac {15 \, x^{7} + 25 \, x^{5} - 115 \, x^{4} - 19 \, x^{3} - 149 \, x^{2} + 25 \, {\left (x^{5} - 5 \, x^{4}\right )} e^{10} + 10 \, {\left (5 \, x^{5} - 24 \, x^{4} - 2 \, x^{3} - 15 \, x^{2}\right )} e^{5} - 21 \, x - 45}{25 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.20, size = 76, normalized size = 2.53 \begin {gather*} \frac {3}{5} \, x + \frac {25 \, x^{5} e^{10} + 50 \, x^{5} e^{5} + 25 \, x^{5} - 125 \, x^{4} e^{10} - 240 \, x^{4} e^{5} - 115 \, x^{4} - 20 \, x^{3} e^{5} - 19 \, x^{3} - 150 \, x^{2} e^{5} - 149 \, x^{2} - 21 \, x - 45}{25 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.07, size = 63, normalized size = 2.10
method | result | size |
risch | \(\frac {3 x}{5}+\frac {\left (50 \,{\mathrm e}^{5}+25 \,{\mathrm e}^{10}+25\right ) x^{5}+\left (-125 \,{\mathrm e}^{10}-240 \,{\mathrm e}^{5}-115\right ) x^{4}+\left (-20 \,{\mathrm e}^{5}-19\right ) x^{3}+\left (-150 \,{\mathrm e}^{5}-149\right ) x^{2}-21 x -45}{25 x^{6}}\) | \(63\) |
norman | \(\frac {-\frac {9}{5}+\left (-6 \,{\mathrm e}^{5}-\frac {149}{25}\right ) x^{2}+\left (-\frac {4 \,{\mathrm e}^{5}}{5}-\frac {19}{25}\right ) x^{3}+\left (-5 \,{\mathrm e}^{10}-\frac {48 \,{\mathrm e}^{5}}{5}-\frac {23}{5}\right ) x^{4}+\left ({\mathrm e}^{10}+2 \,{\mathrm e}^{5}+1\right ) x^{5}-\frac {21 x}{25}+\frac {3 x^{7}}{5}}{x^{6}}\) | \(65\) |
default | \(\frac {3 x}{5}-\frac {21}{25 x^{5}}-\frac {9}{5 x^{6}}-\frac {-50 \,{\mathrm e}^{5}-25 \,{\mathrm e}^{10}-25}{25 x}-\frac {600 \,{\mathrm e}^{5}+596}{100 x^{4}}-\frac {480 \,{\mathrm e}^{5}+250 \,{\mathrm e}^{10}+230}{50 x^{2}}-\frac {60 \,{\mathrm e}^{5}+57}{75 x^{3}}\) | \(67\) |
gosper | \(\frac {25 x^{5} {\mathrm e}^{10}+15 x^{7}-125 x^{4} {\mathrm e}^{10}+50 x^{5} {\mathrm e}^{5}-240 x^{4} {\mathrm e}^{5}+25 x^{5}-20 x^{3} {\mathrm e}^{5}-115 x^{4}-150 x^{2} {\mathrm e}^{5}-19 x^{3}-149 x^{2}-21 x -45}{25 x^{6}}\) | \(82\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.68, size = 64, normalized size = 2.13 \begin {gather*} \frac {3}{5} \, x + \frac {25 \, x^{5} {\left (e^{10} + 2 \, e^{5} + 1\right )} - 5 \, x^{4} {\left (25 \, e^{10} + 48 \, e^{5} + 23\right )} - x^{3} {\left (20 \, e^{5} + 19\right )} - x^{2} {\left (150 \, e^{5} + 149\right )} - 21 \, x - 45}{25 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.18, size = 63, normalized size = 2.10 \begin {gather*} \frac {3\,x}{5}-\frac {\left (-50\,{\mathrm {e}}^5-25\,{\mathrm {e}}^{10}-25\right )\,x^5+\left (240\,{\mathrm {e}}^5+125\,{\mathrm {e}}^{10}+115\right )\,x^4+\left (20\,{\mathrm {e}}^5+19\right )\,x^3+\left (150\,{\mathrm {e}}^5+149\right )\,x^2+21\,x+45}{25\,x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.77, size = 70, normalized size = 2.33 \begin {gather*} \frac {3 x}{5} + \frac {x^{5} \left (25 + 50 e^{5} + 25 e^{10}\right ) + x^{4} \left (- 125 e^{10} - 240 e^{5} - 115\right ) + x^{3} \left (- 20 e^{5} - 19\right ) + x^{2} \left (- 150 e^{5} - 149\right ) - 21 x - 45}{25 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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