Optimal. Leaf size=23 \[ \frac {-2+e^x}{x+\frac {9}{2-2 x-\log (4)}} \]
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Rubi [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 2.36, antiderivative size = 1106, normalized size of antiderivative = 48.09, number of
steps used = 31, number of rules used = 9, integrand size = 112, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {6, 6873,
6820, 6874, 1674, 8, 2302, 2209, 2208} \begin {gather*} \frac {e^{\frac {1}{4} \left (2-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )} (2-\log (4)) \left (2-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right ) \text {ExpIntegralEi}\left (\frac {1}{4} \left (4 x-\sqrt {76-4 \log (4)+\log ^2(4)}+\log (4)-2\right )\right )}{2 \left (76-4 \log (4)+\log ^2(4)\right )}+\frac {1}{2} e^{\frac {1}{4} \left (2-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \left (1-\frac {6-\log (4)}{\sqrt {76-4 \log (4)+\log ^2(4)}}\right ) \text {ExpIntegralEi}\left (\frac {1}{4} \left (4 x-\sqrt {76-4 \log (4)+\log ^2(4)}+\log (4)-2\right )\right )-\frac {e^{\frac {1}{4} \left (2-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \left (40-8 \log (2)+\log ^2(4)\right ) \text {ExpIntegralEi}\left (\frac {1}{4} \left (4 x-\sqrt {76-4 \log (4)+\log ^2(4)}+\log (4)-2\right )\right )}{76-4 \log (4)+\log ^2(4)}+\frac {4 e^{\frac {1}{4} \left (2-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \left (40-8 \log (2)+\log ^2(4)\right ) \text {ExpIntegralEi}\left (\frac {1}{4} \left (4 x-\sqrt {76-4 \log (4)+\log ^2(4)}+\log (4)-2\right )\right )}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2}}-\frac {\sqrt {2} e^{\frac {1}{4} \left (2+\sqrt {76-4 \log (4)+\log ^2(4)}\right )} (2-\log (4))^2 \text {ExpIntegralEi}\left (\frac {1}{4} \left (4 x-\sqrt {76-4 \log (4)+\log ^2(4)}+\log (4)-2\right )\right )}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2}}-\frac {2 (-2 x-\log (4)+2)}{-2 x^2+(2-\log (4)) x+9}+\frac {2 e^x (2-\log (4)) \left (2-\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}\right )}{\left (76-4 \log (4)+\log ^2(4)\right ) \left (-4 x-\sqrt {76-4 \log (4)+\log ^2(4)}-\log (4)+2\right )}-\frac {4 e^x \left (40-8 \log (2)+\log ^2(4)\right )}{\left (76-4 \log (4)+\log ^2(4)\right ) \left (-4 x-\sqrt {76-4 \log (4)+\log ^2(4)}-\log (4)+2\right )}+\frac {2 e^x (2-\log (4)) \left (2-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )}{\left (76-4 \log (4)+\log ^2(4)\right ) \left (-4 x+\sqrt {76-4 \log (4)+\log ^2(4)}-\log (4)+2\right )}-\frac {4 e^x \left (40-8 \log (2)+\log ^2(4)\right )}{\left (76-4 \log (4)+\log ^2(4)\right ) \left (-4 x+\sqrt {76-4 \log (4)+\log ^2(4)}-\log (4)+2\right )}+\frac {e^{\frac {1}{4} \left (2-\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \text {ExpIntegralEi}\left (\frac {1}{4} \left (4 x+\sqrt {76-4 \log (4)+\log ^2(4)}+\log (4)-2\right )\right ) (2-\log (4)) \left (2-\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}\right )}{2 \sqrt {2} \left (76-4 \log (4)+\log ^2(4)\right )}+\frac {1}{2} e^{\frac {1}{4} \left (2-\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \text {ExpIntegralEi}\left (\frac {1}{4} \left (4 x+\sqrt {76-4 \log (4)+\log ^2(4)}+\log (4)-2\right )\right ) \left (1+\frac {6-\log (4)}{\sqrt {76-4 \log (4)+\log ^2(4)}}\right )-\frac {e^{\frac {1}{4} \left (2-\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \text {ExpIntegralEi}\left (\frac {1}{4} \left (4 x+\sqrt {76-4 \log (4)+\log ^2(4)}+\log (4)-2\right )\right ) \left (40-8 \log (2)+\log ^2(4)\right )}{76-4 \log (4)+\log ^2(4)}-\frac {4 e^{\frac {1}{4} \left (2-\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \text {ExpIntegralEi}\left (\frac {1}{4} \left (4 x+\sqrt {76-4 \log (4)+\log ^2(4)}+\log (4)-2\right )\right ) \left (40-8 \log (2)+\log ^2(4)\right )}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2}}+\frac {\sqrt {2} e^{\frac {1}{4} \left (2-\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \text {ExpIntegralEi}\left (\frac {1}{4} \left (4 x+\sqrt {76-4 \log (4)+\log ^2(4)}+\log (4)-2\right )\right ) (2-\log (4))^2}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 8
Rule 1674
Rule 2208
Rule 2209
Rule 2302
Rule 6820
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {44-16 x+8 x^2+(-8+8 x) \log (4)+2 \log ^2(4)+e^x \left (-4-6 x-12 x^2+4 x^3+\left (-5-8 x+4 x^2\right ) \log (4)+(-1+x) \log ^2(4)\right )}{81+36 x-8 x^3+4 x^4+\left (-18 x-4 x^2+4 x^3\right ) \log (4)+x^2 \left (-32+\log ^2(4)\right )} \, dx\\ &=\int \frac {-16 x+8 x^2+(-8+8 x) \log (4)+44 \left (1+\frac {\log ^2(4)}{22}\right )+e^x \left (-4-6 x-12 x^2+4 x^3+\left (-5-8 x+4 x^2\right ) \log (4)+(-1+x) \log ^2(4)\right )}{81+4 x^4+18 x (2-\log (4))-4 x^3 (2-\log (4))-x^2 (8-\log (4)) (4+\log (4))} \, dx\\ &=\int \frac {2 \left (22+4 x^2+4 x (-2+\log (4))-4 \log (4)+\log ^2(4)\right )+e^x \left (-4+4 x^3+4 x^2 (-3+\log (4))-5 \log (4)-\log ^2(4)+x \left (-6-8 \log (4)+\log ^2(4)\right )\right )}{\left (9-2 x^2+x (2-\log (4))\right )^2} \, dx\\ &=\int \left (\frac {2 \left (22+4 x^2-4 x (2-\log (4))-4 \log (4)+\log ^2(4)\right )}{\left (9-2 x^2+x (2-\log (4))\right )^2}+\frac {e^x \left (4 x^3-4 x^2 (3-\log (4))-(1+\log (4)) (4+\log (4))-x \left (6+8 \log (4)-\log ^2(4)\right )\right )}{\left (9-2 x^2+x (2-\log (4))\right )^2}\right ) \, dx\\ &=2 \int \frac {22+4 x^2-4 x (2-\log (4))-4 \log (4)+\log ^2(4)}{\left (9-2 x^2+x (2-\log (4))\right )^2} \, dx+\int \frac {e^x \left (4 x^3-4 x^2 (3-\log (4))-(1+\log (4)) (4+\log (4))-x \left (6+8 \log (4)-\log ^2(4)\right )\right )}{\left (9-2 x^2+x (2-\log (4))\right )^2} \, dx\\ &=-\frac {2 (2-2 x-\log (4))}{9-2 x^2+x (2-\log (4))}-\frac {2 \int 0 \, dx}{76-4 \log (4)+\log ^2(4)}+\int \left (\frac {e^x (4-2 x-\log (4))}{9-2 x^2+x (2-\log (4))}+\frac {e^x \left (-40+2 x (2-\log (4))-\log ^2(4)+\log (256)\right )}{\left (9-2 x^2+x (2-\log (4))\right )^2}\right ) \, dx\\ &=-\frac {2 (2-2 x-\log (4))}{9-2 x^2+x (2-\log (4))}+\int \frac {e^x (4-2 x-\log (4))}{9-2 x^2+x (2-\log (4))} \, dx+\int \frac {e^x \left (-40+2 x (2-\log (4))-\log ^2(4)+\log (256)\right )}{\left (9-2 x^2+x (2-\log (4))\right )^2} \, dx\\ &=-\frac {2 (2-2 x-\log (4))}{9-2 x^2+x (2-\log (4))}+\int \left (\frac {2 e^x x (2-\log (4))}{\left (9-2 x^2+x (2-\log (4))\right )^2}-\frac {40 e^x \left (1+\frac {1}{40} \left (-8 \log (2)+\log ^2(4)\right )\right )}{\left (9-2 x^2+x (2-\log (4))\right )^2}\right ) \, dx+\int \left (\frac {e^x \left (-2+\frac {2 (-6+\log (4))}{\sqrt {76-4 \log (4)+\log ^2(4)}}\right )}{2-4 x-\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}}+\frac {e^x \left (-2-\frac {2 (-6+\log (4))}{\sqrt {76-4 \log (4)+\log ^2(4)}}\right )}{2-4 x-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}}\right ) \, dx\\ &=-\frac {2 (2-2 x-\log (4))}{9-2 x^2+x (2-\log (4))}+(2 (2-\log (4))) \int \frac {e^x x}{\left (9-2 x^2+x (2-\log (4))\right )^2} \, dx-\left (40-8 \log (2)+\log ^2(4)\right ) \int \frac {e^x}{\left (9-2 x^2+x (2-\log (4))\right )^2} \, dx-\left (2 \left (1-\frac {6-\log (4)}{\sqrt {76-4 \log (4)+\log ^2(4)}}\right )\right ) \int \frac {e^x}{2-4 x-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}} \, dx-\left (2 \left (1+\frac {6-\log (4)}{\sqrt {76-4 \log (4)+\log ^2(4)}}\right )\right ) \int \frac {e^x}{2-4 x-\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}} \, dx\\ &=-\frac {2 (2-2 x-\log (4))}{9-2 x^2+x (2-\log (4))}+\frac {1}{2} e^{\frac {1}{4} \left (2-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \text {Ei}\left (\frac {1}{4} \left (-2+4 x+\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}\right )\right ) \left (1-\frac {6-\log (4)}{\sqrt {76-4 \log (4)+\log ^2(4)}}\right )+\frac {1}{2} e^{\frac {1}{4} \left (2-\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \text {Ei}\left (\frac {1}{4} \left (-2+4 x+\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )\right ) \left (1+\frac {6-\log (4)}{\sqrt {76-4 \log (4)+\log ^2(4)}}\right )+(2 (2-\log (4))) \int \left (\frac {4 e^x \left (2-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )}{\left (76-4 \log (4)+\log ^2(4)\right ) \left (2-4 x-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )^2}+\frac {4 e^x (2-\log (4))}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2} \left (2-4 x-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )}+\frac {4 e^x \left (2-\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}\right )}{\left (76-4 \log (4)+\log ^2(4)\right ) \left (-2+4 x+\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )^2}+\frac {4 e^x (2-\log (4))}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2} \left (-2+4 x+\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )}\right ) \, dx-\left (40-8 \log (2)+\log ^2(4)\right ) \int \left (\frac {16 e^x}{\left (76-4 \log (4)+\log ^2(4)\right ) \left (2-4 x-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )^2}+\frac {16 e^x}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2} \left (2-4 x-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )}+\frac {16 e^x}{\left (76-4 \log (4)+\log ^2(4)\right ) \left (-2+4 x+\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )^2}+\frac {16 e^x}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2} \left (-2+4 x+\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )}\right ) \, dx\\ &=-\frac {2 (2-2 x-\log (4))}{9-2 x^2+x (2-\log (4))}+\frac {1}{2} e^{\frac {1}{4} \left (2-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \text {Ei}\left (\frac {1}{4} \left (-2+4 x+\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}\right )\right ) \left (1-\frac {6-\log (4)}{\sqrt {76-4 \log (4)+\log ^2(4)}}\right )+\frac {1}{2} e^{\frac {1}{4} \left (2-\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}\right )} \text {Ei}\left (\frac {1}{4} \left (-2+4 x+\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )\right ) \left (1+\frac {6-\log (4)}{\sqrt {76-4 \log (4)+\log ^2(4)}}\right )+\frac {\left (8 (2-\log (4))^2\right ) \int \frac {e^x}{2-4 x-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}} \, dx}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2}}+\frac {\left (8 (2-\log (4))^2\right ) \int \frac {e^x}{-2+4 x+\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}} \, dx}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2}}-\frac {\left (16 \left (40-8 \log (2)+\log ^2(4)\right )\right ) \int \frac {e^x}{2-4 x-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}} \, dx}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2}}-\frac {\left (16 \left (40-8 \log (2)+\log ^2(4)\right )\right ) \int \frac {e^x}{-2+4 x+\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}} \, dx}{\left (76-4 \log (4)+\log ^2(4)\right )^{3/2}}-\frac {\left (16 \left (40-8 \log (2)+\log ^2(4)\right )\right ) \int \frac {e^x}{\left (2-4 x-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )^2} \, dx}{76-4 \log (4)+\log ^2(4)}-\frac {\left (16 \left (40-8 \log (2)+\log ^2(4)\right )\right ) \int \frac {e^x}{\left (-2+4 x+\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )^2} \, dx}{76-4 \log (4)+\log ^2(4)}+\frac {\left (8 (2-\log (4)) \left (2-\log (4)-\sqrt {76-4 \log (4)+\log ^2(4)}\right )\right ) \int \frac {e^x}{\left (-2+4 x+\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )^2} \, dx}{76-4 \log (4)+\log ^2(4)}+\frac {\left (8 (2-\log (4)) \left (2-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )\right ) \int \frac {e^x}{\left (2-4 x-\log (4)+\sqrt {76-4 \log (4)+\log ^2(4)}\right )^2} \, dx}{76-4 \log (4)+\log ^2(4)}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 28, normalized size = 1.22 \begin {gather*} \frac {\left (-2+e^x\right ) (-2+2 x+\log (4))}{-9+2 x^2+x (-2+\log (4))} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(818\) vs.
\(2(22)=44\).
time = 0.48, size = 819, normalized size = 35.61
method | result | size |
norman | \(\frac {-4 x +\left (2 \ln \left (2\right )-2\right ) {\mathrm e}^{x}+2 \,{\mathrm e}^{x} x +4-4 \ln \left (2\right )}{2 x \ln \left (2\right )+2 x^{2}-2 x -9}\) | \(42\) |
risch | \(\frac {-2 x +2-2 \ln \left (2\right )}{x \ln \left (2\right )+x^{2}-x -\frac {9}{2}}+\frac {2 \left (x +\ln \left (2\right )-1\right ) {\mathrm e}^{x}}{2 x \ln \left (2\right )+2 x^{2}-2 x -9}\) | \(52\) |
default | \(\text {Expression too large to display}\) | \(819\) |
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. 692 vs.
\(2 (21) = 42\).
time = 0.55, size = 692, normalized size = 30.09 \begin {gather*} -4 \, {\left (\frac {2 \, x + \log \left (2\right ) - 1}{2 \, {\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19\right )} x^{2} + 2 \, {\left (\log \left (2\right )^{3} - 3 \, \log \left (2\right )^{2} + 21 \, \log \left (2\right ) - 19\right )} x - 9 \, \log \left (2\right )^{2} + 18 \, \log \left (2\right ) - 171} + \frac {\log \left (\frac {2 \, x - \sqrt {\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19} + \log \left (2\right ) - 1}{2 \, x + \sqrt {\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19} + \log \left (2\right ) - 1}\right )}{{\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19\right )}^{\frac {3}{2}}}\right )} \log \left (2\right )^{2} + 4 \, {\left (\frac {{\left (\log \left (2\right ) - 1\right )} \log \left (\frac {2 \, x - \sqrt {\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19} + \log \left (2\right ) - 1}{2 \, x + \sqrt {\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19} + \log \left (2\right ) - 1}\right )}{{\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19\right )}^{\frac {3}{2}}} + \frac {2 \, {\left (x {\left (\log \left (2\right ) - 1\right )} - 9\right )}}{2 \, {\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19\right )} x^{2} + 2 \, {\left (\log \left (2\right )^{3} - 3 \, \log \left (2\right )^{2} + 21 \, \log \left (2\right ) - 19\right )} x - 9 \, \log \left (2\right )^{2} + 18 \, \log \left (2\right ) - 171}\right )} \log \left (2\right ) + 8 \, {\left (\frac {2 \, x + \log \left (2\right ) - 1}{2 \, {\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19\right )} x^{2} + 2 \, {\left (\log \left (2\right )^{3} - 3 \, \log \left (2\right )^{2} + 21 \, \log \left (2\right ) - 19\right )} x - 9 \, \log \left (2\right )^{2} + 18 \, \log \left (2\right ) - 171} + \frac {\log \left (\frac {2 \, x - \sqrt {\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19} + \log \left (2\right ) - 1}{2 \, x + \sqrt {\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19} + \log \left (2\right ) - 1}\right )}{{\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19\right )}^{\frac {3}{2}}}\right )} \log \left (2\right ) + \frac {2 \, {\left (x + \log \left (2\right ) - 1\right )} e^{x}}{2 \, x^{2} + 2 \, x {\left (\log \left (2\right ) - 1\right )} - 9} - \frac {4 \, {\left (\log \left (2\right ) - 1\right )} \log \left (\frac {2 \, x - \sqrt {\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19} + \log \left (2\right ) - 1}{2 \, x + \sqrt {\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19} + \log \left (2\right ) - 1}\right )}{{\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19\right )}^{\frac {3}{2}}} - \frac {2 \, {\left (2 \, {\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 10\right )} x - 9 \, \log \left (2\right ) + 9\right )}}{2 \, {\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19\right )} x^{2} + 2 \, {\left (\log \left (2\right )^{3} - 3 \, \log \left (2\right )^{2} + 21 \, \log \left (2\right ) - 19\right )} x - 9 \, \log \left (2\right )^{2} + 18 \, \log \left (2\right ) - 171} - \frac {8 \, {\left (x {\left (\log \left (2\right ) - 1\right )} - 9\right )}}{2 \, {\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19\right )} x^{2} + 2 \, {\left (\log \left (2\right )^{3} - 3 \, \log \left (2\right )^{2} + 21 \, \log \left (2\right ) - 19\right )} x - 9 \, \log \left (2\right )^{2} + 18 \, \log \left (2\right ) - 171} - \frac {22 \, {\left (2 \, x + \log \left (2\right ) - 1\right )}}{2 \, {\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19\right )} x^{2} + 2 \, {\left (\log \left (2\right )^{3} - 3 \, \log \left (2\right )^{2} + 21 \, \log \left (2\right ) - 19\right )} x - 9 \, \log \left (2\right )^{2} + 18 \, \log \left (2\right ) - 171} - \frac {4 \, \log \left (\frac {2 \, x - \sqrt {\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19} + \log \left (2\right ) - 1}{2 \, x + \sqrt {\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19} + \log \left (2\right ) - 1}\right )}{{\left (\log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 19\right )}^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 36, normalized size = 1.57 \begin {gather*} \frac {2 \, {\left ({\left (x + \log \left (2\right ) - 1\right )} e^{x} - 2 \, x - 2 \, \log \left (2\right ) + 2\right )}}{2 \, x^{2} + 2 \, x \log \left (2\right ) - 2 \, x - 9} \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. 54 vs.
\(2 (17) = 34\).
time = 0.35, size = 54, normalized size = 2.35 \begin {gather*} \frac {- 4 x - 4 \log {\left (2 \right )} + 4}{2 x^{2} + x \left (-2 + 2 \log {\left (2 \right )}\right ) - 9} + \frac {\left (2 x - 2 + 2 \log {\left (2 \right )}\right ) e^{x}}{2 x^{2} - 2 x + 2 x \log {\left (2 \right )} - 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 41, normalized size = 1.78 \begin {gather*} \frac {2 \, {\left (x e^{x} + e^{x} \log \left (2\right ) - 2 \, x - e^{x} - 2 \, \log \left (2\right ) + 2\right )}}{2 \, x^{2} + 2 \, x \log \left (2\right ) - 2 \, x - 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {2\,\ln \left (2\right )\,\left (8\,x-8\right )-16\,x-{\mathrm {e}}^x\,\left (6\,x-4\,{\ln \left (2\right )}^2\,\left (x-1\right )+2\,\ln \left (2\right )\,\left (-4\,x^2+8\,x+5\right )+12\,x^2-4\,x^3+4\right )+8\,{\ln \left (2\right )}^2+8\,x^2+44}{36\,x+4\,x^2\,{\ln \left (2\right )}^2-2\,\ln \left (2\right )\,\left (-4\,x^3+4\,x^2+18\,x\right )-32\,x^2-8\,x^3+4\,x^4+81} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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