Optimal. Leaf size=30 \[ \frac {x}{3-\left (6+5 e^{-21-x}-x\right ) \log \left (-e^4+x\right )} \]
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Rubi [F]
time = 48.92, 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 {-5 e^{21+x} x+e^{42+2 x} \left (3 e^4-9 x+x^2\right )+\left (e^{42+2 x} \left (-6 e^4+6 x\right )+e^{21+x} \left (e^4 (-5-5 x)+5 x+5 x^2\right )\right ) \log \left (-e^4+x\right )}{e^{42+2 x} \left (9 e^4-9 x\right )+\left (e^{21+x} \left (-30 e^4+30 x\right )+e^{42+2 x} \left (36 x-6 x^2+e^4 (-36+6 x)\right )\right ) \log \left (-e^4+x\right )+\left (25 e^4-25 x+e^{21+x} \left (e^4 (60-10 x)-60 x+10 x^2\right )+e^{42+2 x} \left (-36 x+12 x^2-x^3+e^4 \left (36-12 x+x^2\right )\right )\right ) \log ^2\left (-e^4+x\right )} \, 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^{21+x} \left (-5 x+e^{21+x} \left (3 e^4+(-9+x) x\right )-\left (e^4-x\right ) \left (5+6 e^{21+x}+5 x\right ) \log \left (-e^4+x\right )\right )}{\left (e^4-x\right ) \left (3 e^{21+x}+\left (-5+e^{21+x} (-6+x)\right ) \log \left (-e^4+x\right )\right )^2} \, dx\\ &=\int \left (\frac {e^{21+x} \left (3 e^4-9 x+x^2-6 e^4 \log \left (-e^4+x\right )+6 x \log \left (-e^4+x\right )\right )}{\left (e^4-x\right ) \left (3-6 \log \left (-e^4+x\right )+x \log \left (-e^4+x\right )\right ) \left (3 e^{21+x}-5 \log \left (-e^4+x\right )-6 e^{21+x} \log \left (-e^4+x\right )+e^{21+x} x \log \left (-e^4+x\right )\right )}+\frac {5 e^{21+x} x \left (-3-3 e^4 \log \left (-e^4+x\right )+3 x \log \left (-e^4+x\right )+5 e^4 \log ^2\left (-e^4+x\right )-5 \left (1+\frac {e^4}{5}\right ) x \log ^2\left (-e^4+x\right )+x^2 \log ^2\left (-e^4+x\right )\right )}{\left (e^4-x\right ) \left (3-6 \log \left (-e^4+x\right )+x \log \left (-e^4+x\right )\right ) \left (3 e^{21+x}-5 \log \left (-e^4+x\right )-6 e^{21+x} \log \left (-e^4+x\right )+e^{21+x} x \log \left (-e^4+x\right )\right )^2}\right ) \, dx\\ &=5 \int \frac {e^{21+x} x \left (-3-3 e^4 \log \left (-e^4+x\right )+3 x \log \left (-e^4+x\right )+5 e^4 \log ^2\left (-e^4+x\right )-5 \left (1+\frac {e^4}{5}\right ) x \log ^2\left (-e^4+x\right )+x^2 \log ^2\left (-e^4+x\right )\right )}{\left (e^4-x\right ) \left (3-6 \log \left (-e^4+x\right )+x \log \left (-e^4+x\right )\right ) \left (3 e^{21+x}-5 \log \left (-e^4+x\right )-6 e^{21+x} \log \left (-e^4+x\right )+e^{21+x} x \log \left (-e^4+x\right )\right )^2} \, dx+\int \frac {e^{21+x} \left (3 e^4-9 x+x^2-6 e^4 \log \left (-e^4+x\right )+6 x \log \left (-e^4+x\right )\right )}{\left (e^4-x\right ) \left (3-6 \log \left (-e^4+x\right )+x \log \left (-e^4+x\right )\right ) \left (3 e^{21+x}-5 \log \left (-e^4+x\right )-6 e^{21+x} \log \left (-e^4+x\right )+e^{21+x} x \log \left (-e^4+x\right )\right )} \, dx\\ &=5 \int \frac {e^{21+x} x \left (-3-3 \left (e^4-x\right ) \log \left (-e^4+x\right )-\left (e^4-x\right ) (-5+x) \log ^2\left (-e^4+x\right )\right )}{\left (e^4-x\right ) \left (3 e^{21+x}+\left (-5+e^{21+x} (-6+x)\right ) \log \left (-e^4+x\right )\right )^2 \left (3+(-6+x) \log \left (-e^4+x\right )\right )} \, dx+\int \frac {e^{21+x} \left (3 e^4+(-9+x) x-6 \left (e^4-x\right ) \log \left (-e^4+x\right )\right )}{\left (e^4-x\right ) \left (3 e^{21+x}+\left (-5+e^{21+x} (-6+x)\right ) \log \left (-e^4+x\right )\right ) \left (3+(-6+x) \log \left (-e^4+x\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.38, size = 37, normalized size = 1.23 \begin {gather*} \frac {e^{21+x} x}{3 e^{21+x}+\left (-5+e^{21+x} (-6+x)\right ) \log \left (-e^4+x\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.27, size = 51, normalized size = 1.70
method | result | size |
risch | \(\frac {x \,{\mathrm e}^{x +21}}{{\mathrm e}^{x +21} \ln \left (x -{\mathrm e}^{4}\right ) x -6 \,{\mathrm e}^{x +21} \ln \left (x -{\mathrm e}^{4}\right )+3 \,{\mathrm e}^{x +21}-5 \ln \left (x -{\mathrm e}^{4}\right )}\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.48, size = 37, normalized size = 1.23 \begin {gather*} \frac {x e^{\left (x + 21\right )}}{{\left ({\left (x e^{21} - 6 \, e^{21}\right )} e^{x} - 5\right )} \log \left (x - e^{4}\right ) + 3 \, e^{\left (x + 21\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 33, normalized size = 1.10 \begin {gather*} \frac {x e^{\left (x + 21\right )}}{{\left ({\left (x - 6\right )} e^{\left (x + 21\right )} - 5\right )} \log \left (x - e^{4}\right ) + 3 \, e^{\left (x + 21\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 112 vs.
\(2 (20) = 40\).
time = 0.43, size = 112, normalized size = 3.73 \begin {gather*} \frac {5 x \log {\left (x - e^{4} \right )}}{- 5 x \log {\left (x - e^{4} \right )}^{2} + \left (x^{2} \log {\left (x - e^{4} \right )}^{2} - 12 x \log {\left (x - e^{4} \right )}^{2} + 6 x \log {\left (x - e^{4} \right )} + 36 \log {\left (x - e^{4} \right )}^{2} - 36 \log {\left (x - e^{4} \right )} + 9\right ) e^{x + 21} + 30 \log {\left (x - e^{4} \right )}^{2} - 15 \log {\left (x - e^{4} \right )}} + \frac {x}{\left (x - 6\right ) \log {\left (x - e^{4} \right )} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 62 vs.
\(2 (25) = 50\).
time = 0.65, size = 62, normalized size = 2.07 \begin {gather*} \frac {{\left (x + 21\right )} e^{\left (x + 21\right )} - 21 \, e^{\left (x + 21\right )}}{{\left (x + 21\right )} e^{\left (x + 21\right )} \log \left (x - e^{4}\right ) - 27 \, e^{\left (x + 21\right )} \log \left (x - e^{4}\right ) + 3 \, e^{\left (x + 21\right )} - 5 \, \log \left (x - e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.74, size = 285, normalized size = 9.50 \begin {gather*} \frac {25\,x\,{\mathrm {e}}^{x+25}+60\,x\,{\mathrm {e}}^{2\,x+46}+15\,x\,{\mathrm {e}}^{2\,x+50}+36\,x\,{\mathrm {e}}^{3\,x+67}+3\,x\,{\mathrm {e}}^{3\,x+71}-25\,x^2\,{\mathrm {e}}^{x+21}-60\,x^2\,{\mathrm {e}}^{2\,x+42}+25\,x^3\,{\mathrm {e}}^{2\,x+42}-40\,x^2\,{\mathrm {e}}^{2\,x+46}-36\,x^2\,{\mathrm {e}}^{3\,x+63}+15\,x^3\,{\mathrm {e}}^{3\,x+63}-x^4\,{\mathrm {e}}^{3\,x+63}-18\,x^2\,{\mathrm {e}}^{3\,x+67}+x^3\,{\mathrm {e}}^{3\,x+67}}{\left (3\,{\mathrm {e}}^{x+21}-\ln \left (x-{\mathrm {e}}^4\right )\,\left (6\,{\mathrm {e}}^{x+21}-x\,{\mathrm {e}}^{x+21}+5\right )\right )\,\left (60\,{\mathrm {e}}^{x+25}-25\,x+15\,{\mathrm {e}}^{x+29}+25\,{\mathrm {e}}^4+36\,{\mathrm {e}}^{2\,x+46}+3\,{\mathrm {e}}^{2\,x+50}-60\,x\,{\mathrm {e}}^{x+21}-40\,x\,{\mathrm {e}}^{x+25}-36\,x\,{\mathrm {e}}^{2\,x+42}-18\,x\,{\mathrm {e}}^{2\,x+46}+25\,x^2\,{\mathrm {e}}^{x+21}+15\,x^2\,{\mathrm {e}}^{2\,x+42}-x^3\,{\mathrm {e}}^{2\,x+42}+x^2\,{\mathrm {e}}^{2\,x+46}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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