Optimal. Leaf size=27 \[ \frac {5 \left (-2-e^{\left (\frac {3+2 x}{x}\right )^{5 x}}+x\right )}{2 x} \]
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Rubi [F] time = 2.64, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {30+20 x+e^{\left (\frac {3+2 x}{x}\right )^{5 x}} \left (15+10 x+\left (\frac {3+2 x}{x}\right )^{5 x} \left (75 x+\left (-75 x-50 x^2\right ) \log \left (\frac {3+2 x}{x}\right )\right )\right )}{6 x^2+4 x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {30+20 x+e^{\left (\frac {3+2 x}{x}\right )^{5 x}} \left (15+10 x+\left (\frac {3+2 x}{x}\right )^{5 x} \left (75 x+\left (-75 x-50 x^2\right ) \log \left (\frac {3+2 x}{x}\right )\right )\right )}{x^2 (6+4 x)} \, dx\\ &=\int \left (\frac {5 \left (2+e^{\left (2+\frac {3}{x}\right )^{5 x}}\right )}{2 x^2}-\frac {25 e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x} \left (-3+3 \log \left (2+\frac {3}{x}\right )+2 x \log \left (2+\frac {3}{x}\right )\right )}{2 x (3+2 x)}\right ) \, dx\\ &=\frac {5}{2} \int \frac {2+e^{\left (2+\frac {3}{x}\right )^{5 x}}}{x^2} \, dx-\frac {25}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x} \left (-3+3 \log \left (2+\frac {3}{x}\right )+2 x \log \left (2+\frac {3}{x}\right )\right )}{x (3+2 x)} \, dx\\ &=\frac {5}{2} \int \left (\frac {2}{x^2}+\frac {e^{\left (2+\frac {3}{x}\right )^{5 x}}}{x^2}\right ) \, dx-\frac {25}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x} \left (-3+(3+2 x) \log \left (2+\frac {3}{x}\right )\right )}{x (3+2 x)} \, dx\\ &=-\frac {5}{x}+\frac {5}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}}}{x^2} \, dx-\frac {25}{2} \int \left (-\frac {3 e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x (3+2 x)}+\frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x} \log \left (2+\frac {3}{x}\right )}{x}\right ) \, dx\\ &=-\frac {5}{x}+\frac {5}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}}}{x^2} \, dx-\frac {25}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x} \log \left (2+\frac {3}{x}\right )}{x} \, dx+\frac {75}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x (3+2 x)} \, dx\\ &=-\frac {5}{x}+\frac {5}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}}}{x^2} \, dx+\frac {25}{2} \int \frac {3 \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx}{(-3-2 x) x} \, dx+\frac {75}{2} \int \left (\frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{3 x}-\frac {2 e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{3 (3+2 x)}\right ) \, dx-\frac {1}{2} \left (25 \log \left (2+\frac {3}{x}\right )\right ) \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx\\ &=-\frac {5}{x}+\frac {5}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}}}{x^2} \, dx+\frac {25}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx-25 \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{3+2 x} \, dx+\frac {75}{2} \int \frac {\int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx}{(-3-2 x) x} \, dx-\frac {1}{2} \left (25 \log \left (2+\frac {3}{x}\right )\right ) \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx\\ &=-\frac {5}{x}+\frac {5}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}}}{x^2} \, dx+\frac {25}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx-25 \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{3+2 x} \, dx+\frac {75}{2} \int \left (-\frac {\int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx}{3 x}+\frac {2 \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx}{3 (3+2 x)}\right ) \, dx-\frac {1}{2} \left (25 \log \left (2+\frac {3}{x}\right )\right ) \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx\\ &=-\frac {5}{x}+\frac {5}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}}}{x^2} \, dx+\frac {25}{2} \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx-\frac {25}{2} \int \frac {\int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx}{x} \, dx-25 \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{3+2 x} \, dx+25 \int \frac {\int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx}{3+2 x} \, dx-\frac {1}{2} \left (25 \log \left (2+\frac {3}{x}\right )\right ) \int \frac {e^{\left (2+\frac {3}{x}\right )^{5 x}} \left (2+\frac {3}{x}\right )^{5 x}}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.81, size = 22, normalized size = 0.81 \begin {gather*} -\frac {5 \left (2+e^{\left (2+\frac {3}{x}\right )^{5 x}}\right )}{2 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 21, normalized size = 0.78 \begin {gather*} -\frac {5 \, {\left (e^{\left (\left (\frac {2 \, x + 3}{x}\right )^{5 \, x}\right )} + 2\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {5 \, {\left ({\left (5 \, {\left ({\left (2 \, x^{2} + 3 \, x\right )} \log \left (\frac {2 \, x + 3}{x}\right ) - 3 \, x\right )} \left (\frac {2 \, x + 3}{x}\right )^{5 \, x} - 2 \, x - 3\right )} e^{\left (\left (\frac {2 \, x + 3}{x}\right )^{5 \, x}\right )} - 4 \, x - 6\right )}}{2 \, {\left (2 \, x^{3} + 3 \, x^{2}\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 26, normalized size = 0.96
method | result | size |
risch | \(-\frac {5}{x}-\frac {5 \,{\mathrm e}^{\left (\frac {2 x +3}{x}\right )^{5 x}}}{2 x}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 28, normalized size = 1.04 \begin {gather*} -\frac {5 \, e^{\left (e^{\left (5 \, x \log \left (2 \, x + 3\right ) - 5 \, x \log \relax (x)\right )}\right )}}{2 \, x} - \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.45, size = 19, normalized size = 0.70 \begin {gather*} -\frac {5\,\left ({\mathrm {e}}^{{\left (\frac {3}{x}+2\right )}^{5\,x}}+2\right )}{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.00, size = 24, normalized size = 0.89 \begin {gather*} - \frac {5 e^{e^{5 x \log {\left (\frac {2 x + 3}{x} \right )}}}}{2 x} - \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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