Optimal. Leaf size=18 \[ \frac {5}{2} e^4 \left (\frac {1}{x}+\frac {x^2}{9}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.17, number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 14} \begin {gather*} \frac {5 e^4 x^2}{18}+\frac {5 e^4}{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}{18} e^4 \int \frac {-45+10 x^3}{x^2} \, dx\\ &=\frac {1}{18} e^4 \int \left (-\frac {45}{x^2}+10 x\right ) \, dx\\ &=\frac {5 e^4}{2 x}+\frac {5 e^4 x^2}{18}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.89 \begin {gather*} \frac {5}{18} e^4 \left (\frac {9}{x}+x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 12, normalized size = 0.67 \begin {gather*} \frac {5 \, {\left (x^{3} + 9\right )} e^{4}}{18 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 13, normalized size = 0.72 \begin {gather*} \frac {5}{18} \, {\left (x^{2} + \frac {9}{x}\right )} e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 13, normalized size = 0.72
method | result | size |
gosper | \(\frac {5 \,{\mathrm e}^{4} \left (x^{3}+9\right )}{18 x}\) | \(13\) |
default | \(\frac {5 \,{\mathrm e}^{4} \left (x^{2}+\frac {9}{x}\right )}{18}\) | \(14\) |
risch | \(\frac {5 x^{2} {\mathrm e}^{4}}{18}+\frac {5 \,{\mathrm e}^{4}}{2 x}\) | \(16\) |
norman | \(\frac {\frac {5 x^{3} {\mathrm e}^{4}}{18}+\frac {5 \,{\mathrm e}^{4}}{2}}{x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 13, normalized size = 0.72 \begin {gather*} \frac {5}{18} \, {\left (x^{2} + \frac {9}{x}\right )} e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.23, size = 12, normalized size = 0.67 \begin {gather*} \frac {5\,{\mathrm {e}}^4\,\left (x^3+9\right )}{18\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 17, normalized size = 0.94 \begin {gather*} \frac {5 x^{2} e^{4}}{18} + \frac {5 e^{4}}{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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