Optimal. Leaf size=26 \[ 3-e^{\frac {20 x (x+\log (5))}{\frac {2}{3}+2 (1+2 x)}} \]
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Rubi [A] time = 0.44, antiderivative size = 28, normalized size of antiderivative = 1.08, number of steps used = 3, number of rules used = 3, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {27, 6741, 6706} \begin {gather*} -5^{\frac {60 x}{12 x+8}} e^{\frac {15 x^2}{3 x+2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 6706
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {4 \left (15 x^2+15 x \log (5)\right )}{8+12 x}} \left (-60 x-45 x^2-30 \log (5)\right )}{(2+3 x)^2} \, dx\\ &=\int \frac {e^{\frac {4 x (15 x+15 \log (5))}{8+12 x}} \left (-60 x-45 x^2-30 \log (5)\right )}{(2+3 x)^2} \, dx\\ &=-5^{\frac {60 x}{8+12 x}} e^{\frac {15 x^2}{2+3 x}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 36, normalized size = 1.38 \begin {gather*} -\frac {5^{\frac {15 x}{2+3 x}} e^{\frac {15 x^2}{2+3 x}} \log (25)}{2 \log (5)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 20, normalized size = 0.77 \begin {gather*} -e^{\left (\frac {15 \, {\left (x^{2} + x \log \relax (5)\right )}}{3 \, x + 2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 28, normalized size = 1.08 \begin {gather*} -e^{\left (\frac {15 \, x^{2}}{3 \, x + 2} + \frac {15 \, x \log \relax (5)}{3 \, x + 2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 18, normalized size = 0.69
method | result | size |
risch | \(-{\mathrm e}^{\frac {15 x \left (\ln \relax (5)+x \right )}{3 x +2}}\) | \(18\) |
gosper | \(-{\mathrm e}^{\frac {15 x \left (\ln \relax (5)+x \right )}{3 x +2}}\) | \(20\) |
norman | \(\frac {-2 \,{\mathrm e}^{\frac {60 x \ln \relax (5)+60 x^{2}}{12 x +8}}-3 x \,{\mathrm e}^{\frac {60 x \ln \relax (5)+60 x^{2}}{12 x +8}}}{3 x +2}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 28, normalized size = 1.08 \begin {gather*} -3125 \, e^{\left (5 \, x - \frac {10 \, \log \relax (5)}{3 \, x + 2} + \frac {20}{3 \, {\left (3 \, x + 2\right )}} - \frac {10}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.29, size = 27, normalized size = 1.04 \begin {gather*} -5^{\frac {15\,x}{3\,x+2}}\,{\mathrm {e}}^{\frac {15\,x^2}{3\,x+2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 19, normalized size = 0.73 \begin {gather*} - e^{\frac {4 \left (15 x^{2} + 15 x \log {\relax (5 )}\right )}{12 x + 8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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