Optimal. Leaf size=32 \[ \left (-x+\frac {x}{25-x}-\log \left (-e^2+\frac {e}{x}-2 x\right )\right )^2 \]
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Rubi [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 6.15, antiderivative size = 791, normalized size of antiderivative = 24.72, number of steps
used = 62, number of rules used = 24, integrand size = 237, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.101, Rules used = {6820, 12,
6860, 1642, 648, 632, 212, 642, 2608, 2603, 1671, 2605, 2604, 2404, 2338, 2353, 2352, 2354, 2438,
2465, 2441, 2437, 2440, 2439} \begin {gather*} -2 \text {PolyLog}\left (2,-\frac {4 x-\sqrt {e \left (8+e^3\right )}+e^2}{2 \sqrt {e \left (8+e^3\right )}}\right )-2 \text {PolyLog}\left (2,\frac {4 x+\sqrt {e \left (8+e^3\right )}+e^2}{2 \sqrt {e \left (8+e^3\right )}}\right )+x^2-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (-2 x^2-e^2 x+e\right )}{2 \left (1250-e+25 e^2\right )}+\frac {25 \left (100+e^2\right ) \log \left (-2 x^2-e^2 x+e\right )}{1250-e+25 e^2}+\frac {1}{2} e^2 \log \left (-2 x^2-e^2 x+e\right )+2 x-\frac {1300}{25-x}+\frac {625}{(25-x)^2}-\log ^2(x)-\log ^2\left (4 x-\sqrt {e \left (8+e^3\right )}+e^2\right )-\log ^2\left (4 x+\sqrt {e \left (8+e^3\right )}+e^2\right )+2 x \log \left (-2 x+\frac {e}{x}-e^2\right )-\frac {50 \log \left (-2 x+\frac {e}{x}-e^2\right )}{25-x}-2 \log \left (-2 x+\frac {e}{x}-e^2\right ) \log (x)+2 \log \left (e^2+\sqrt {e \left (8+e^3\right )}\right ) \log (x)-2 \log (x)+2 \log \left (-2 x+\frac {e}{x}-e^2\right ) \log \left (4 x-\sqrt {e \left (8+e^3\right )}+e^2\right )+2 \log \left (-\frac {4 x}{e^2-\sqrt {e \left (8+e^3\right )}}\right ) \log \left (4 x-\sqrt {e \left (8+e^3\right )}+e^2\right )+2 \log \left (\frac {1}{4} \left (\sqrt {e \left (8+e^3\right )}-e^2\right )\right ) \log \left (4 x-\sqrt {e \left (8+e^3\right )}+e^2\right )+2 \log \left (-2 x+\frac {e}{x}-e^2\right ) \log \left (4 x+\sqrt {e \left (8+e^3\right )}+e^2\right )-2 \log \left (-\frac {4 x-\sqrt {e \left (8+e^3\right )}+e^2}{2 \sqrt {e \left (8+e^3\right )}}\right ) \log \left (4 x+\sqrt {e \left (8+e^3\right )}+e^2\right )-2 \log \left (4 x-\sqrt {e \left (8+e^3\right )}+e^2\right ) \log \left (\frac {4 x+\sqrt {e \left (8+e^3\right )}+e^2}{2 \sqrt {e \left (8+e^3\right )}}\right )+2 \log (x) \log \left (\frac {4 x}{e^2+\sqrt {e \left (8+e^3\right )}}+1\right )-\frac {50 \sqrt {e \left (8+e^3\right )} \tanh ^{-1}\left (\frac {4 x+e^2}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}+\sqrt {e \left (8+e^3\right )} \tanh ^{-1}\left (\frac {4 x+e^2}{\sqrt {e \left (8+e^3\right )}}\right )-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \tanh ^{-1}\left (\frac {4 x+e^2}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2} \end {gather*}
Warning: Unable to verify antiderivative.
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Rule 12
Rule 212
Rule 632
Rule 642
Rule 648
Rule 1642
Rule 1671
Rule 2338
Rule 2352
Rule 2353
Rule 2354
Rule 2404
Rule 2437
Rule 2438
Rule 2439
Rule 2440
Rule 2441
Rule 2465
Rule 2603
Rule 2604
Rule 2605
Rule 2608
Rule 6820
Rule 6860
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (e^2 x^2 \left (600-50 x+x^2\right )-e \left (-625+650 x-51 x^2+x^3\right )+2 x^2 \left (625+550 x-49 x^2+x^3\right )\right ) \left ((-24+x) x+(-25+x) \log \left (-e^2+\frac {e}{x}-2 x\right )\right )}{(25-x)^3 x \left (e-e^2 x-2 x^2\right )} \, dx\\ &=2 \int \frac {\left (e^2 x^2 \left (600-50 x+x^2\right )-e \left (-625+650 x-51 x^2+x^3\right )+2 x^2 \left (625+550 x-49 x^2+x^3\right )\right ) \left ((-24+x) x+(-25+x) \log \left (-e^2+\frac {e}{x}-2 x\right )\right )}{(25-x)^3 x \left (e-e^2 x-2 x^2\right )} \, dx\\ &=2 \int \left (\frac {(24-x) \left (-625 e+650 e x-1250 \left (1+\frac {3 e (17+200 e)}{1250}\right ) x^2-1100 \left (1-\frac {e (1+50 e)}{1100}\right ) x^3+98 \left (1-\frac {e^2}{98}\right ) x^4-2 x^5\right )}{(25-x)^3 \left (e-e^2 x-2 x^2\right )}+\frac {\left (-625 e+650 e x-1250 \left (1+\frac {3 e (17+200 e)}{1250}\right ) x^2-1100 \left (1-\frac {e (1+50 e)}{1100}\right ) x^3+98 \left (1-\frac {e^2}{98}\right ) x^4-2 x^5\right ) \log \left (-e^2+\frac {e}{x}-2 x\right )}{(25-x)^2 x \left (e-e^2 x-2 x^2\right )}\right ) \, dx\\ &=2 \int \frac {(24-x) \left (-625 e+650 e x-1250 \left (1+\frac {3 e (17+200 e)}{1250}\right ) x^2-1100 \left (1-\frac {e (1+50 e)}{1100}\right ) x^3+98 \left (1-\frac {e^2}{98}\right ) x^4-2 x^5\right )}{(25-x)^3 \left (e-e^2 x-2 x^2\right )} \, dx+2 \int \frac {\left (-625 e+650 e x-1250 \left (1+\frac {3 e (17+200 e)}{1250}\right ) x^2-1100 \left (1-\frac {e (1+50 e)}{1100}\right ) x^3+98 \left (1-\frac {e^2}{98}\right ) x^4-2 x^5\right ) \log \left (-e^2+\frac {e}{x}-2 x\right )}{(25-x)^2 x \left (e-e^2 x-2 x^2\right )} \, dx\\ &=2 \int \left (2-\frac {625}{(-25+x)^3}-\frac {650}{(-25+x)^2}+\frac {1250+e}{\left (1250-e+25 e^2\right ) (-25+x)}+x+\frac {e \left (-2400+2 e-49 e^2+\left (4+1200 e-e^2+25 e^3\right ) x\right )}{\left (1250-e+25 e^2\right ) \left (e-e^2 x-2 x^2\right )}\right ) \, dx+2 \int \left (\log \left (-e^2+\frac {e}{x}-2 x\right )-\frac {25 \log \left (-e^2+\frac {e}{x}-2 x\right )}{(-25+x)^2}-\frac {\log \left (-e^2+\frac {e}{x}-2 x\right )}{x}+\frac {\left (e^2+4 x\right ) \log \left (-e^2+\frac {e}{x}-2 x\right )}{-e+e^2 x+2 x^2}\right ) \, dx\\ &=\frac {625}{(25-x)^2}-\frac {1300}{25-x}+4 x+x^2+\frac {2 (1250+e) \log (25-x)}{1250-e+25 e^2}+2 \int \log \left (-e^2+\frac {e}{x}-2 x\right ) \, dx-2 \int \frac {\log \left (-e^2+\frac {e}{x}-2 x\right )}{x} \, dx+2 \int \frac {\left (e^2+4 x\right ) \log \left (-e^2+\frac {e}{x}-2 x\right )}{-e+e^2 x+2 x^2} \, dx-50 \int \frac {\log \left (-e^2+\frac {e}{x}-2 x\right )}{(-25+x)^2} \, dx+\frac {(2 e) \int \frac {-2400+2 e-49 e^2+\left (4+1200 e-e^2+25 e^3\right ) x}{e-e^2 x-2 x^2} \, dx}{1250-e+25 e^2}\\ &=\frac {625}{(25-x)^2}-\frac {1300}{25-x}+4 x+x^2-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )+\frac {2 (1250+e) \log (25-x)}{1250-e+25 e^2}-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-2 \int \frac {-e-2 x^2}{e-e^2 x-2 x^2} \, dx+2 \int \left (\frac {4 \log \left (-e^2+\frac {e}{x}-2 x\right )}{e^2-\sqrt {e \left (8+e^3\right )}+4 x}+\frac {4 \log \left (-e^2+\frac {e}{x}-2 x\right )}{e^2+\sqrt {e \left (8+e^3\right )}+4 x}\right ) \, dx+2 \int \frac {\left (-2-\frac {e}{x^2}\right ) \log (x)}{-e^2+\frac {e}{x}-2 x} \, dx-50 \int \frac {e+2 x^2}{(25-x) x \left (e-e^2 x-2 x^2\right )} \, dx-\frac {\left (e (2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right )\right ) \int \frac {1}{e-e^2 x-2 x^2} \, dx}{2 \left (1250-e+25 e^2\right )}-\frac {\left (e \left (4+1200 e-e^2+25 e^3\right )\right ) \int \frac {-e^2-4 x}{e-e^2 x-2 x^2} \, dx}{2 \left (1250-e+25 e^2\right )}\\ &=\frac {625}{(25-x)^2}-\frac {1300}{25-x}+4 x+x^2-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )+\frac {2 (1250+e) \log (25-x)}{1250-e+25 e^2}-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}-2 \int \left (1-\frac {2 e-e^2 x}{e-e^2 x-2 x^2}\right ) \, dx+2 \int \left (-\frac {\log (x)}{x}+\frac {\left (e^2+4 x\right ) \log (x)}{-e+e^2 x+2 x^2}\right ) \, dx+8 \int \frac {\log \left (-e^2+\frac {e}{x}-2 x\right )}{e^2-\sqrt {e \left (8+e^3\right )}+4 x} \, dx+8 \int \frac {\log \left (-e^2+\frac {e}{x}-2 x\right )}{e^2+\sqrt {e \left (8+e^3\right )}+4 x} \, dx-50 \int \left (\frac {1250+e}{25 \left (1250-e+25 e^2\right ) (-25+x)}+\frac {1}{25 x}+\frac {e \left (4+50 e+e^3\right )+2 \left (100+e^2\right ) x}{\left (1250-e+25 e^2\right ) \left (e-e^2 x-2 x^2\right )}\right ) \, dx+\frac {\left (e (2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right )\right ) \text {Subst}\left (\int \frac {1}{e \left (8+e^3\right )-x^2} \, dx,x,-e^2-4 x\right )}{1250-e+25 e^2}\\ &=\frac {625}{(25-x)^2}-\frac {1300}{25-x}+2 x+x^2-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \tanh ^{-1}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )-2 \log (x)-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}+2 \int \frac {2 e-e^2 x}{e-e^2 x-2 x^2} \, dx-2 \int \frac {\log (x)}{x} \, dx+2 \int \frac {\left (e^2+4 x\right ) \log (x)}{-e+e^2 x+2 x^2} \, dx-2 \int \frac {\left (-2-\frac {e}{x^2}\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e^2+\frac {e}{x}-2 x} \, dx-2 \int \frac {\left (-2-\frac {e}{x^2}\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e^2+\frac {e}{x}-2 x} \, dx-\frac {50 \int \frac {e \left (4+50 e+e^3\right )+2 \left (100+e^2\right ) x}{e-e^2 x-2 x^2} \, dx}{1250-e+25 e^2}\\ &=\frac {625}{(25-x)^2}-\frac {1300}{25-x}+2 x+x^2-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \tanh ^{-1}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )-2 \log (x)-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-\log ^2(x)+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}+2 \int \left (\frac {4 \log (x)}{e^2-\sqrt {e \left (8+e^3\right )}+4 x}+\frac {4 \log (x)}{e^2+\sqrt {e \left (8+e^3\right )}+4 x}\right ) \, dx-2 \int \left (-\frac {\log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{x}+\frac {\left (e^2+4 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e+e^2 x+2 x^2}\right ) \, dx-2 \int \left (-\frac {\log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{x}+\frac {\left (e^2+4 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e+e^2 x+2 x^2}\right ) \, dx+\frac {1}{2} e^2 \int \frac {-e^2-4 x}{e-e^2 x-2 x^2} \, dx+\frac {\left (25 \left (100+e^2\right )\right ) \int \frac {-e^2-4 x}{e-e^2 x-2 x^2} \, dx}{1250-e+25 e^2}+\frac {1}{2} \left (e \left (8+e^3\right )\right ) \int \frac {1}{e-e^2 x-2 x^2} \, dx-\frac {\left (25 e \left (8+e^3\right )\right ) \int \frac {1}{e-e^2 x-2 x^2} \, dx}{1250-e+25 e^2}\\ &=\frac {625}{(25-x)^2}-\frac {1300}{25-x}+2 x+x^2-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \tanh ^{-1}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )-2 \log (x)-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-\log ^2(x)+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )+\frac {1}{2} e^2 \log \left (e-e^2 x-2 x^2\right )+\frac {25 \left (100+e^2\right ) \log \left (e-e^2 x-2 x^2\right )}{1250-e+25 e^2}-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}+2 \int \frac {\log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{x} \, dx-2 \int \frac {\left (e^2+4 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e+e^2 x+2 x^2} \, dx+2 \int \frac {\log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{x} \, dx-2 \int \frac {\left (e^2+4 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e+e^2 x+2 x^2} \, dx+8 \int \frac {\log (x)}{e^2-\sqrt {e \left (8+e^3\right )}+4 x} \, dx+8 \int \frac {\log (x)}{e^2+\sqrt {e \left (8+e^3\right )}+4 x} \, dx-\left (e \left (8+e^3\right )\right ) \text {Subst}\left (\int \frac {1}{e \left (8+e^3\right )-x^2} \, dx,x,-e^2-4 x\right )+\frac {\left (50 e \left (8+e^3\right )\right ) \text {Subst}\left (\int \frac {1}{e \left (8+e^3\right )-x^2} \, dx,x,-e^2-4 x\right )}{1250-e+25 e^2}\\ &=\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. \(96\) vs. \(2(32)=64\).
time = 0.14, size = 96, normalized size = 3.00 \begin {gather*} 2 \left (\frac {625}{2 (-25+x)^2}+\frac {650}{-25+x}+x+\frac {x^2}{2}+\frac {\left (25-25 x+x^2\right ) \log \left (-e^2+\frac {e}{x}-2 x\right )}{-25+x}+\frac {1}{2} \log ^2\left (-e^2+\frac {e}{x}-2 x\right )-\log (x)+\log \left (-e+e^2 x+2 x^2\right )\right ) \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. \(155\) vs.
\(2(32)=64\).
time = 1.33, size = 156, normalized size = 4.88
method | result | size |
norman | \(\frac {x^{4}+x^{2} \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right )^{2}+28800 x -98 \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right ) x^{2}+1200 x \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right )-48 x^{3}+625 \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right )^{2}-50 x \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right )^{2}-360000+2 \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right ) x^{3}}{\left (x -25\right )^{2}}\) | \(156\) |
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. 123 vs.
\(2 (26) = 52\).
time = 0.72, size = 123, normalized size = 3.84 \begin {gather*} \frac {x^{4} - 48 \, x^{3} + {\left (x^{2} - 50 \, x + 625\right )} \log \left (-2 \, x^{2} - x e^{2} + e\right )^{2} + {\left (x^{2} - 50 \, x + 625\right )} \log \left (x\right )^{2} + 525 \, x^{2} + 2 \, {\left (x^{3} - 49 \, x^{2} - {\left (x^{2} - 50 \, x + 625\right )} \log \left (x\right ) + 600 \, x\right )} \log \left (-2 \, x^{2} - x e^{2} + e\right ) - 2 \, {\left (x^{3} - 49 \, x^{2} + 600 \, x\right )} \log \left (x\right ) + 2550 \, x - 31875}{x^{2} - 50 \, x + 625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 94 vs.
\(2 (26) = 52\).
time = 0.42, size = 94, normalized size = 2.94 \begin {gather*} \frac {x^{4} - 48 \, x^{3} + {\left (x^{2} - 50 \, x + 625\right )} \log \left (-\frac {2 \, x^{2} + x e^{2} - e}{x}\right )^{2} + 525 \, x^{2} + 2 \, {\left (x^{3} - 49 \, x^{2} + 600 \, x\right )} \log \left (-\frac {2 \, x^{2} + x e^{2} - e}{x}\right ) + 2550 \, x - 31875}{x^{2} - 50 \, x + 625} \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. 92 vs.
\(2 (20) = 40\).
time = 3.02, size = 92, normalized size = 2.88 \begin {gather*} x^{2} + 2 x + \frac {1300 x - 31875}{x^{2} - 50 x + 625} - 2 \log {\left (x \right )} + \log {\left (\frac {- 2 x^{2} - x e^{2} + e}{x} \right )}^{2} + 2 \log {\left (x^{2} + \frac {x e^{2}}{2} - \frac {e}{2} \right )} + \frac {\left (2 x^{2} - 50 x + 50\right ) \log {\left (\frac {- 2 x^{2} - x e^{2} + e}{x} \right )}}{x - 25} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.38, size = 98, normalized size = 3.06 \begin {gather*} 2\,x-48\,\ln \left (x^2+\frac {{\mathrm {e}}^2\,x}{2}-\frac {\mathrm {e}}{2}\right )+48\,\ln \left (x\right )+\frac {1300\,x-31875}{x^2-50\,x+625}+{\ln \left (-\frac {2\,x^2+{\mathrm {e}}^2\,x-\mathrm {e}}{x}\right )}^2+x^2+\frac {\ln \left (-\frac {2\,x^2+{\mathrm {e}}^2\,x-\mathrm {e}}{x}\right )\,\left (x^2-600\right )}{\frac {x}{2}-\frac {25}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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