3.90.35 \(\int \frac {e^{-4+\frac {25+40 \log (-3+x^2)+e^{4+e^x} x \log ^2(-3+x^2)+(16+e^4 x^2) \log ^2(-3+x^2)}{e^4 x \log ^2(-3+x^2)}} (-100 x^2+(75-105 x^2) \log (-3+x^2)+(120-40 x^2) \log ^2(-3+x^2)+e^{4+e^x+x} (-3 x^2+x^4) \log ^3(-3+x^2)+(48-16 x^2+e^4 (-3 x^2+x^4)) \log ^3(-3+x^2))}{(-3 x^2+x^4) \log ^3(-3+x^2)} \, dx\)

Optimal. Leaf size=30 \[ e^{e^{e^x}+x+\frac {\left (4+\frac {5}{\log \left (-3+x^2\right )}\right )^2}{e^4 x}} \]

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Rubi [F]  time = 58.10, 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 {\exp \left (-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-4 + (25 + 40*Log[-3 + x^2] + E^(4 + E^x)*x*Log[-3 + x^2]^2 + (16 + E^4*x^2)*Log[-3 + x^2]^2)/(E^4*x*L
og[-3 + x^2]^2))*(-100*x^2 + (75 - 105*x^2)*Log[-3 + x^2] + (120 - 40*x^2)*Log[-3 + x^2]^2 + E^(4 + E^x + x)*(
-3*x^2 + x^4)*Log[-3 + x^2]^3 + (48 - 16*x^2 + E^4*(-3*x^2 + x^4))*Log[-3 + x^2]^3))/((-3*x^2 + x^4)*Log[-3 +
x^2]^3),x]

[Out]

Defer[Int][E^(E^E^x + 16/(E^4*x) + x + 25/(E^4*x*Log[-3 + x^2]^2) + 40/(E^4*x*Log[-3 + x^2])), x] + Defer[Int]
[E^(E^x + x + (25 + 40*Log[-3 + x^2] + E^(4 + E^x)*x*Log[-3 + x^2]^2 + (16 + E^4*x^2)*Log[-3 + x^2]^2)/(E^4*x*
Log[-3 + x^2]^2)), x] - 16*Defer[Int][E^(-4 + E^E^x + 16/(E^4*x) + x + 25/(E^4*x*Log[-3 + x^2]^2) + 40/(E^4*x*
Log[-3 + x^2]))/x^2, x] + (50*Defer[Int][E^(-4 + E^E^x + 16/(E^4*x) + x + 25/(E^4*x*Log[-3 + x^2]^2) + 40/(E^4
*x*Log[-3 + x^2]))/((Sqrt[3] - x)*Log[-3 + x^2]^3), x])/Sqrt[3] + (50*Defer[Int][E^(-4 + E^E^x + 16/(E^4*x) +
x + 25/(E^4*x*Log[-3 + x^2]^2) + 40/(E^4*x*Log[-3 + x^2]))/((Sqrt[3] + x)*Log[-3 + x^2]^3), x])/Sqrt[3] + (40*
Defer[Int][E^(-4 + E^E^x + 16/(E^4*x) + x + 25/(E^4*x*Log[-3 + x^2]^2) + 40/(E^4*x*Log[-3 + x^2]))/((Sqrt[3] -
x)*Log[-3 + x^2]^2), x])/Sqrt[3] - 25*Defer[Int][E^(-4 + E^E^x + 16/(E^4*x) + x + 25/(E^4*x*Log[-3 + x^2]^2)
+ 40/(E^4*x*Log[-3 + x^2]))/(x^2*Log[-3 + x^2]^2), x] + (40*Defer[Int][E^(-4 + E^E^x + 16/(E^4*x) + x + 25/(E^
4*x*Log[-3 + x^2]^2) + 40/(E^4*x*Log[-3 + x^2]))/((Sqrt[3] + x)*Log[-3 + x^2]^2), x])/Sqrt[3] - 40*Defer[Int][
E^(-4 + E^E^x + 16/(E^4*x) + x + 25/(E^4*x*Log[-3 + x^2]^2) + 40/(E^4*x*Log[-3 + x^2]))/(x^2*Log[-3 + x^2]), x
]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{x^2 \left (-3+x^2\right ) \log ^3\left (-3+x^2\right )} \, dx\\ &=\int \left (\exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right )+\frac {\exp \left (-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \left (100 x^2-75 \log \left (-3+x^2\right )+105 x^2 \log \left (-3+x^2\right )-120 \log ^2\left (-3+x^2\right )+40 x^2 \log ^2\left (-3+x^2\right )-48 \log ^3\left (-3+x^2\right )+16 \left (1+\frac {3 e^4}{16}\right ) x^2 \log ^3\left (-3+x^2\right )-e^4 x^4 \log ^3\left (-3+x^2\right )\right )}{x^2 \left (3-x^2\right ) \log ^3\left (-3+x^2\right )}\right ) \, dx\\ &=\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx+\int \frac {\exp \left (-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \left (100 x^2-75 \log \left (-3+x^2\right )+105 x^2 \log \left (-3+x^2\right )-120 \log ^2\left (-3+x^2\right )+40 x^2 \log ^2\left (-3+x^2\right )-48 \log ^3\left (-3+x^2\right )+16 \left (1+\frac {3 e^4}{16}\right ) x^2 \log ^3\left (-3+x^2\right )-e^4 x^4 \log ^3\left (-3+x^2\right )\right )}{x^2 \left (3-x^2\right ) \log ^3\left (-3+x^2\right )} \, dx\\ &=\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx+\int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \left (100 x^2+15 \left (-5+7 x^2\right ) \log \left (-3+x^2\right )+40 \left (-3+x^2\right ) \log ^2\left (-3+x^2\right )-\left (-3+x^2\right ) \left (-16+e^4 x^2\right ) \log ^3\left (-3+x^2\right )\right )}{x^2 \left (3-x^2\right ) \log ^3\left (-3+x^2\right )} \, dx\\ &=\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx+\int \left (\frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \left (-16+e^4 x^2\right )}{x^2}-\frac {100 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (-3+x^2\right ) \log ^3\left (-3+x^2\right )}-\frac {15 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \left (-5+7 x^2\right )}{x^2 \left (-3+x^2\right ) \log ^2\left (-3+x^2\right )}-\frac {40 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )}\right ) \, dx\\ &=-\left (15 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \left (-5+7 x^2\right )}{x^2 \left (-3+x^2\right ) \log ^2\left (-3+x^2\right )} \, dx\right )-40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )} \, dx-100 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (-3+x^2\right ) \log ^3\left (-3+x^2\right )} \, dx+\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx+\int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \left (-16+e^4 x^2\right )}{x^2} \, dx\\ &=-\left (15 \int \left (\frac {5 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{3 x^2 \log ^2\left (-3+x^2\right )}+\frac {16 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{3 \left (-3+x^2\right ) \log ^2\left (-3+x^2\right )}\right ) \, dx\right )-40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )} \, dx-100 \int \left (-\frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{2 \sqrt {3} \left (\sqrt {3}-x\right ) \log ^3\left (-3+x^2\right )}-\frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{2 \sqrt {3} \left (\sqrt {3}+x\right ) \log ^3\left (-3+x^2\right )}\right ) \, dx+\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx+\int \left (\exp \left (e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )-\frac {16 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2}\right ) \, dx\\ &=-\left (16 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2} \, dx\right )-25 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log ^2\left (-3+x^2\right )} \, dx-40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )} \, dx-80 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (-3+x^2\right ) \log ^2\left (-3+x^2\right )} \, dx+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}-x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}+x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\int \exp \left (e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \, dx+\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx\\ &=-\left (16 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2} \, dx\right )-25 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log ^2\left (-3+x^2\right )} \, dx-40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )} \, dx-80 \int \left (-\frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{2 \sqrt {3} \left (\sqrt {3}-x\right ) \log ^2\left (-3+x^2\right )}-\frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{2 \sqrt {3} \left (\sqrt {3}+x\right ) \log ^2\left (-3+x^2\right )}\right ) \, dx+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}-x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}+x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\int \exp \left (e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \, dx+\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx\\ &=-\left (16 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2} \, dx\right )-25 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log ^2\left (-3+x^2\right )} \, dx-40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )} \, dx+\frac {40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}-x\right ) \log ^2\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\frac {40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}+x\right ) \log ^2\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}-x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}+x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\int \exp \left (e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \, dx+\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.28, size = 49, normalized size = 1.63 \begin {gather*} e^{e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-4 + (25 + 40*Log[-3 + x^2] + E^(4 + E^x)*x*Log[-3 + x^2]^2 + (16 + E^4*x^2)*Log[-3 + x^2]^2)/(E
^4*x*Log[-3 + x^2]^2))*(-100*x^2 + (75 - 105*x^2)*Log[-3 + x^2] + (120 - 40*x^2)*Log[-3 + x^2]^2 + E^(4 + E^x
+ x)*(-3*x^2 + x^4)*Log[-3 + x^2]^3 + (48 - 16*x^2 + E^4*(-3*x^2 + x^4))*Log[-3 + x^2]^3))/((-3*x^2 + x^4)*Log
[-3 + x^2]^3),x]

[Out]

E^(E^E^x + 16/(E^4*x) + x + 25/(E^4*x*Log[-3 + x^2]^2) + 40/(E^4*x*Log[-3 + x^2]))

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fricas [B]  time = 0.52, size = 75, normalized size = 2.50 \begin {gather*} e^{\left (\frac {{\left (x e^{\left (x + e^{x} + 4\right )} \log \left (x^{2} - 3\right )^{2} + {\left ({\left (x^{2} - 4 \, x\right )} e^{4} + 16\right )} e^{x} \log \left (x^{2} - 3\right )^{2} + 40 \, e^{x} \log \left (x^{2} - 3\right ) + 25 \, e^{x}\right )} e^{\left (-x - 4\right )}}{x \log \left (x^{2} - 3\right )^{2}} + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^4-3*x^2)*exp(4)*exp(x)*log(x^2-3)^3*exp(exp(x))+((x^4-3*x^2)*exp(4)-16*x^2+48)*log(x^2-3)^3+(-40
*x^2+120)*log(x^2-3)^2+(-105*x^2+75)*log(x^2-3)-100*x^2)*exp((x*exp(4)*log(x^2-3)^2*exp(exp(x))+(x^2*exp(4)+16
)*log(x^2-3)^2+40*log(x^2-3)+25)/x/exp(4)/log(x^2-3)^2)/(x^4-3*x^2)/exp(4)/log(x^2-3)^3,x, algorithm="fricas")

[Out]

e^((x*e^(x + e^x + 4)*log(x^2 - 3)^2 + ((x^2 - 4*x)*e^4 + 16)*e^x*log(x^2 - 3)^2 + 40*e^x*log(x^2 - 3) + 25*e^
x)*e^(-x - 4)/(x*log(x^2 - 3)^2) + 4)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^4-3*x^2)*exp(4)*exp(x)*log(x^2-3)^3*exp(exp(x))+((x^4-3*x^2)*exp(4)-16*x^2+48)*log(x^2-3)^3+(-40
*x^2+120)*log(x^2-3)^2+(-105*x^2+75)*log(x^2-3)-100*x^2)*exp((x*exp(4)*log(x^2-3)^2*exp(exp(x))+(x^2*exp(4)+16
)*log(x^2-3)^2+40*log(x^2-3)+25)/x/exp(4)/log(x^2-3)^2)/(x^4-3*x^2)/exp(4)/log(x^2-3)^3,x, algorithm="giac")

[Out]

undef

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maple [B]  time = 0.49, size = 65, normalized size = 2.17

method	result	size
risch	\({\mathrm e}^{\frac {\left ({\mathrm e}^{4} \ln \left (x^{2}-3\right )^{2} x^{2}+x \ln \left (x^{2}-3\right )^{2} {\mathrm e}^{{\mathrm e}^{x}+4}+16 \ln \left (x^{2}-3\right )^{2}+40 \ln \left (x^{2}-3\right )+25\right ) {\mathrm e}^{-4}}{x \ln \left (x^{2}-3\right )^{2}}}\)	\(65\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^4-3*x^2)*exp(4)*exp(x)*ln(x^2-3)^3*exp(exp(x))+((x^4-3*x^2)*exp(4)-16*x^2+48)*ln(x^2-3)^3+(-40*x^2+120
)*ln(x^2-3)^2+(-105*x^2+75)*ln(x^2-3)-100*x^2)*exp((x*exp(4)*ln(x^2-3)^2*exp(exp(x))+(x^2*exp(4)+16)*ln(x^2-3)
^2+40*ln(x^2-3)+25)/x/exp(4)/ln(x^2-3)^2)/(x^4-3*x^2)/exp(4)/ln(x^2-3)^3,x,method=_RETURNVERBOSE)

[Out]

exp((exp(4)*ln(x^2-3)^2*x^2+x*ln(x^2-3)^2*exp(exp(x)+4)+16*ln(x^2-3)^2+40*ln(x^2-3)+25)*exp(-4)/x/ln(x^2-3)^2)

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maxima [A]  time = 0.62, size = 43, normalized size = 1.43 \begin {gather*} e^{\left (x + \frac {16 \, e^{\left (-4\right )}}{x} + \frac {40 \, e^{\left (-4\right )}}{x \log \left (x^{2} - 3\right )} + \frac {25 \, e^{\left (-4\right )}}{x \log \left (x^{2} - 3\right )^{2}} + e^{\left (e^{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^4-3*x^2)*exp(4)*exp(x)*log(x^2-3)^3*exp(exp(x))+((x^4-3*x^2)*exp(4)-16*x^2+48)*log(x^2-3)^3+(-40
*x^2+120)*log(x^2-3)^2+(-105*x^2+75)*log(x^2-3)-100*x^2)*exp((x*exp(4)*log(x^2-3)^2*exp(exp(x))+(x^2*exp(4)+16
)*log(x^2-3)^2+40*log(x^2-3)+25)/x/exp(4)/log(x^2-3)^2)/(x^4-3*x^2)/exp(4)/log(x^2-3)^3,x, algorithm="maxima")

[Out]

e^(x + 16*e^(-4)/x + 40*e^(-4)/(x*log(x^2 - 3)) + 25*e^(-4)/(x*log(x^2 - 3)^2) + e^(e^x))

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mupad [B]  time = 7.43, size = 47, normalized size = 1.57 \begin {gather*} {\mathrm {e}}^{\frac {16\,{\mathrm {e}}^{-4}}{x}}\,{\mathrm {e}}^{\frac {25\,{\mathrm {e}}^{-4}}{x\,{\ln \left (x^2-3\right )}^2}}\,{\mathrm {e}}^{\frac {40\,{\mathrm {e}}^{-4}}{x\,\ln \left (x^2-3\right )}}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((exp(-4)*(40*log(x^2 - 3) + log(x^2 - 3)^2*(x^2*exp(4) + 16) + x*exp(exp(x))*exp(4)*log(x^2 - 3)^2 +
25))/(x*log(x^2 - 3)^2))*exp(-4)*(log(x^2 - 3)^3*(exp(4)*(3*x^2 - x^4) + 16*x^2 - 48) + log(x^2 - 3)*(105*x^2
- 75) + 100*x^2 + log(x^2 - 3)^2*(40*x^2 - 120) + exp(exp(x))*exp(4)*exp(x)*log(x^2 - 3)^3*(3*x^2 - x^4)))/(lo
g(x^2 - 3)^3*(3*x^2 - x^4)),x)

[Out]

exp((16*exp(-4))/x)*exp((25*exp(-4))/(x*log(x^2 - 3)^2))*exp((40*exp(-4))/(x*log(x^2 - 3)))*exp(exp(exp(x)))*e
xp(x)

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sympy [B]  time = 4.21, size = 60, normalized size = 2.00 \begin {gather*} e^{\frac {x e^{4} e^{e^{x}} \log {\left (x^{2} - 3 \right )}^{2} + \left (x^{2} e^{4} + 16\right ) \log {\left (x^{2} - 3 \right )}^{2} + 40 \log {\left (x^{2} - 3 \right )} + 25}{x e^{4} \log {\left (x^{2} - 3 \right )}^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**4-3*x**2)*exp(4)*exp(x)*ln(x**2-3)**3*exp(exp(x))+((x**4-3*x**2)*exp(4)-16*x**2+48)*ln(x**2-3)*
*3+(-40*x**2+120)*ln(x**2-3)**2+(-105*x**2+75)*ln(x**2-3)-100*x**2)*exp((x*exp(4)*ln(x**2-3)**2*exp(exp(x))+(x
**2*exp(4)+16)*ln(x**2-3)**2+40*ln(x**2-3)+25)/x/exp(4)/ln(x**2-3)**2)/(x**4-3*x**2)/exp(4)/ln(x**2-3)**3,x)

[Out]

exp((x*exp(4)*exp(exp(x))*log(x**2 - 3)**2 + (x**2*exp(4) + 16)*log(x**2 - 3)**2 + 40*log(x**2 - 3) + 25)*exp(
-4)/(x*log(x**2 - 3)**2))

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