Optimal. Leaf size=23 \[ \frac {3}{x}+e^{\frac {9}{5 x^3}} \left (2 x+x^2\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 20, normalized size of antiderivative = 0.87, number of steps used = 4, number of rules used = 3, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 14, 2288} \begin {gather*} e^{\frac {9}{5 x^3}} x (x+2)+\frac {3}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {-15 x+e^{\frac {9}{5 x^3}} \left (-54-27 x+10 x^3+10 x^4\right )}{x^3} \, dx\\ &=\frac {1}{5} \int \left (-\frac {15}{x^2}+\frac {e^{\frac {9}{5 x^3}} \left (-54-27 x+10 x^3+10 x^4\right )}{x^3}\right ) \, dx\\ &=\frac {3}{x}+\frac {1}{5} \int \frac {e^{\frac {9}{5 x^3}} \left (-54-27 x+10 x^3+10 x^4\right )}{x^3} \, dx\\ &=\frac {3}{x}+e^{\frac {9}{5 x^3}} x (2+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 25, normalized size = 1.09 \begin {gather*} \frac {1}{5} \left (\frac {15}{x}+5 e^{\frac {9}{5 x^3}} x (2+x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.92, size = 22, normalized size = 0.96 \begin {gather*} \frac {{\left (x^{3} + 2 \, x^{2}\right )} e^{\left (\frac {9}{5 \, x^{3}}\right )} + 3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.44, size = 27, normalized size = 1.17 \begin {gather*} \frac {x^{3} e^{\left (\frac {9}{5 \, x^{3}}\right )} + 2 \, x^{2} e^{\left (\frac {9}{5 \, x^{3}}\right )} + 3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 24, normalized size = 1.04
method | result | size |
risch | \(\frac {3}{x}+\frac {\left (5 x^{2}+10 x \right ) {\mathrm e}^{\frac {9}{5 x^{3}}}}{5}\) | \(24\) |
norman | \(\frac {{\mathrm e}^{\frac {9}{5 x^{3}}} x^{4}+3 x +2 \,{\mathrm e}^{\frac {9}{5 x^{3}}} x^{3}}{x^{2}}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.45, size = 92, normalized size = 4.00 \begin {gather*} \frac {2}{3} \, \left (\frac {9}{5}\right )^{\frac {2}{3}} x^{2} \left (-\frac {1}{x^{3}}\right )^{\frac {2}{3}} \Gamma \left (-\frac {2}{3}, -\frac {9}{5 \, x^{3}}\right ) + \frac {2}{3} \, \left (\frac {9}{5}\right )^{\frac {1}{3}} x \left (-\frac {1}{x^{3}}\right )^{\frac {1}{3}} \Gamma \left (-\frac {1}{3}, -\frac {9}{5 \, x^{3}}\right ) - \frac {\left (\frac {9}{5}\right )^{\frac {2}{3}} \Gamma \left (\frac {1}{3}, -\frac {9}{5 \, x^{3}}\right )}{x \left (-\frac {1}{x^{3}}\right )^{\frac {1}{3}}} + \frac {3}{x} - \frac {2 \, \left (\frac {9}{5}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}, -\frac {9}{5 \, x^{3}}\right )}{x^{2} \left (-\frac {1}{x^{3}}\right )^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.46, size = 25, normalized size = 1.09 \begin {gather*} 2\,x\,{\mathrm {e}}^{\frac {9}{5\,x^3}}+x^2\,{\mathrm {e}}^{\frac {9}{5\,x^3}}+\frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 17, normalized size = 0.74 \begin {gather*} \left (x^{2} + 2 x\right ) e^{\frac {9}{5 x^{3}}} + \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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