Optimal. Leaf size=30 \[ \frac {e^{\frac {e^{3+\frac {1}{4} \left (5+e^4\right )-x}}{5-3 x}}}{x} \]
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Rubi [B] time = 1.80, antiderivative size = 107, normalized size of antiderivative = 3.57, number of steps used = 3, number of rules used = 3, integrand size = 78, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {1594, 27, 2288} \begin {gather*} -\frac {\left (2 x-3 x^2\right ) \exp \left (\frac {1}{4} \left (-4 x+e^4+17\right )+\frac {e^{\frac {1}{4} \left (-4 x+e^4+17\right )}}{5-3 x}\right )}{\left (\frac {3 e^{\frac {1}{4} \left (-4 x+e^4+17\right )}}{(5-3 x)^2}-\frac {e^{\frac {1}{4} \left (-4 x+e^4+17\right )}}{5-3 x}\right ) (5-3 x)^2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1594
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-\frac {e^{\frac {1}{4} \left (17+e^4-4 x\right )}}{-5+3 x}} \left (-25+30 x-9 x^2+e^{\frac {1}{4} \left (17+e^4-4 x\right )} \left (-2 x+3 x^2\right )\right )}{x^2 \left (25-30 x+9 x^2\right )} \, dx\\ &=\int \frac {e^{-\frac {e^{\frac {1}{4} \left (17+e^4-4 x\right )}}{-5+3 x}} \left (-25+30 x-9 x^2+e^{\frac {1}{4} \left (17+e^4-4 x\right )} \left (-2 x+3 x^2\right )\right )}{x^2 (-5+3 x)^2} \, dx\\ &=-\frac {\exp \left (\frac {1}{4} \left (17+e^4-4 x\right )+\frac {e^{\frac {1}{4} \left (17+e^4-4 x\right )}}{5-3 x}\right ) \left (2 x-3 x^2\right )}{\left (\frac {3 e^{\frac {1}{4} \left (17+e^4-4 x\right )}}{(5-3 x)^2}-\frac {e^{\frac {1}{4} \left (17+e^4-4 x\right )}}{5-3 x}\right ) (5-3 x)^2 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.55, size = 30, normalized size = 1.00 \begin {gather*} \frac {e^{-\frac {e^{\frac {1}{4} \left (17+e^4\right )-x}}{-5+3 x}}}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 24, normalized size = 0.80 \begin {gather*} \frac {e^{\left (-\frac {e^{\left (-x + \frac {1}{4} \, e^{4} + \frac {17}{4}\right )}}{3 \, x - 5}\right )}}{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 {{\left (9 \, x^{2} - {\left (3 \, x^{2} - 2 \, x\right )} e^{\left (-x + \frac {1}{4} \, e^{4} + \frac {17}{4}\right )} - 30 \, x + 25\right )} e^{\left (-\frac {e^{\left (-x + \frac {1}{4} \, e^{4} + \frac {17}{4}\right )}}{3 \, x - 5}\right )}}{9 \, x^{4} - 30 \, x^{3} + 25 \, x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 25, normalized size = 0.83
method | result | size |
risch | \(\frac {{\mathrm e}^{-\frac {{\mathrm e}^{\frac {{\mathrm e}^{4}}{4}-x +\frac {17}{4}}}{3 x -5}}}{x}\) | \(25\) |
norman | \(\frac {3 x \,{\mathrm e}^{-\frac {{\mathrm e}^{\frac {{\mathrm e}^{4}}{4}-x +\frac {17}{4}}}{3 x -5}}-5 \,{\mathrm e}^{-\frac {{\mathrm e}^{\frac {{\mathrm e}^{4}}{4}-x +\frac {17}{4}}}{3 x -5}}}{x \left (3 x -5\right )}\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\int \frac {{\left (9 \, x^{2} - {\left (3 \, x^{2} - 2 \, x\right )} e^{\left (-x + \frac {1}{4} \, e^{4} + \frac {17}{4}\right )} - 30 \, x + 25\right )} e^{\left (-\frac {e^{\left (-x + \frac {1}{4} \, e^{4} + \frac {17}{4}\right )}}{3 \, x - 5}\right )}}{9 \, x^{4} - 30 \, x^{3} + 25 \, x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.41, size = 25, normalized size = 0.83 \begin {gather*} \frac {{\mathrm {e}}^{-\frac {{\mathrm {e}}^{\frac {{\mathrm {e}}^4}{4}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{17/4}}{3\,x-5}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 20, normalized size = 0.67 \begin {gather*} \frac {e^{- \frac {e^{- x + \frac {17}{4} + \frac {e^{4}}{4}}}{3 x - 5}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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