Optimal. Leaf size=25 \[ \frac {1}{2 \left (3-e^{2 (5-x)^4}+\log (-2+x)\right )} \]
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Rubi [F]
time = 24.63, 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 {-1+e^{1250-1000 x+300 x^2-40 x^3+2 x^4} \left (2000-2200 x+840 x^2-136 x^3+8 x^4\right )}{-36+e^{1250-1000 x+300 x^2-40 x^3+2 x^4} (24-12 x)+18 x+e^{2500-2000 x+600 x^2-80 x^3+4 x^4} (-4+2 x)+\left (-24+e^{1250-1000 x+300 x^2-40 x^3+2 x^4} (8-4 x)+12 x\right ) \log (-2+x)+(-4+2 x) \log ^2(-2+x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{80 x \left (25+x^2\right )} \left (1-8 e^{2 (-5+x)^4} (-5+x)^3 (-2+x)\right )}{2 (2-x) \left (3 e^{40 x \left (25+x^2\right )}-e^{2 \left (625+150 x^2+x^4\right )}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx\\ &=\frac {1}{2} \int \frac {e^{80 x \left (25+x^2\right )} \left (1-8 e^{2 (-5+x)^4} (-5+x)^3 (-2+x)\right )}{(2-x) \left (3 e^{40 x \left (25+x^2\right )}-e^{2 \left (625+150 x^2+x^4\right )}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx\\ &=\frac {1}{2} \int \left (-\frac {e^{80 x \left (25+x^2\right )}}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2}+\frac {2000 e^{2 (-5+x)^4+80 x \left (25+x^2\right )}}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2}-\frac {2200 e^{2 (-5+x)^4+80 x \left (25+x^2\right )} x}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2}+\frac {840 e^{2 (-5+x)^4+80 x \left (25+x^2\right )} x^2}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2}-\frac {136 e^{2 (-5+x)^4+80 x \left (25+x^2\right )} x^3}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2}+\frac {8 e^{2 (-5+x)^4+80 x \left (25+x^2\right )} x^4}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2}\right ) \, dx\\ &=-\left (\frac {1}{2} \int \frac {e^{80 x \left (25+x^2\right )}}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx\right )+4 \int \frac {e^{2 (-5+x)^4+80 x \left (25+x^2\right )} x^4}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx-68 \int \frac {e^{2 (-5+x)^4+80 x \left (25+x^2\right )} x^3}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx+420 \int \frac {e^{2 (-5+x)^4+80 x \left (25+x^2\right )} x^2}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx+1000 \int \frac {e^{2 (-5+x)^4+80 x \left (25+x^2\right )}}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx-1100 \int \frac {e^{2 (-5+x)^4+80 x \left (25+x^2\right )} x}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx\\ &=-\left (\frac {1}{2} \int \frac {e^{80 x \left (25+x^2\right )}}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx\right )+4 \int \frac {e^{1250+1000 x+300 x^2+40 x^3+2 x^4} x^4}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx-68 \int \frac {e^{1250+1000 x+300 x^2+40 x^3+2 x^4} x^3}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx+420 \int \frac {e^{1250+1000 x+300 x^2+40 x^3+2 x^4} x^2}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx+1000 \int \frac {e^{1250+1000 x+300 x^2+40 x^3+2 x^4}}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx-1100 \int \frac {e^{1250+1000 x+300 x^2+40 x^3+2 x^4} x}{(-2+x) \left (3 e^{40 x \left (25+x^2\right )}-e^{1250+300 x^2+2 x^4}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(60\) vs. \(2(25)=50\).
time = 0.27, size = 60, normalized size = 2.40 \begin {gather*} \frac {e^{40 x \left (25+x^2\right )}}{2 \left (3 e^{40 x \left (25+x^2\right )}-e^{2 \left (625+150 x^2+x^4\right )}+e^{40 x \left (25+x^2\right )} \log (-2+x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 21, normalized size = 0.84
method | result | size |
risch | \(-\frac {1}{2 \left ({\mathrm e}^{2 \left (x -5\right )^{4}}-\ln \left (x -2\right )-3\right )}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 53 vs.
\(2 (20) = 40\).
time = 0.37, size = 53, normalized size = 2.12 \begin {gather*} \frac {e^{\left (40 \, x^{3} + 1000 \, x\right )}}{2 \, {\left ({\left (e^{\left (1000 \, x\right )} \log \left (x - 2\right ) + 3 \, e^{\left (1000 \, x\right )}\right )} e^{\left (40 \, x^{3}\right )} - e^{\left (2 \, x^{4} + 300 \, x^{2} + 1250\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 33, normalized size = 1.32 \begin {gather*} -\frac {1}{2 \, {\left (e^{\left (2 \, x^{4} - 40 \, x^{3} + 300 \, x^{2} - 1000 \, x + 1250\right )} - \log \left (x - 2\right ) - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.18, size = 34, normalized size = 1.36 \begin {gather*} - \frac {1}{2 e^{2 x^{4} - 40 x^{3} + 300 x^{2} - 1000 x + 1250} - 2 \log {\left (x - 2 \right )} - 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.83, size = 33, normalized size = 1.32 \begin {gather*} -\frac {1}{2 \, {\left (e^{\left (2 \, x^{4} - 40 \, x^{3} + 300 \, x^{2} - 1000 \, x + 1250\right )} - \log \left (x - 2\right ) - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.07, size = 36, normalized size = 1.44 \begin {gather*} \frac {1}{2\,\left (\ln \left (x-2\right )-{\mathrm {e}}^{-1000\,x}\,{\mathrm {e}}^{1250}\,{\mathrm {e}}^{2\,x^4}\,{\mathrm {e}}^{-40\,x^3}\,{\mathrm {e}}^{300\,x^2}+3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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