3.91.31 \(\int \frac {e^{\log ^2(\frac {-25+e^{2+2 x}+e^{2+x} (-40-8 x)-10 x-x^2+e^2 (525+185 x+11 x^2-x^3)}{e^2 (25+10 x+x^2)})} (e^{2+2 x} (16+4 x)+e^{2+x} (-320-144 x-16 x^2)+e^2 (-250-150 x-30 x^2-2 x^3)) \log (\frac {-25+e^{2+2 x}+e^{2+x} (-40-8 x)-10 x-x^2+e^2 (525+185 x+11 x^2-x^3)}{e^2 (25+10 x+x^2)})}{-125-75 x-15 x^2-x^3+e^{2+2 x} (5+x)+e^{2+x} (-200-80 x-8 x^2)+e^2 (2625+1450 x+240 x^2+6 x^3-x^4)} \, dx\)

Optimal. Leaf size=28 \[ e^{\log ^2\left (5-\frac {1}{e^2}-x+\left (-4+\frac {e^x}{5+x}\right )^2\right )} \]

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Rubi [F]  time = 100.78, 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 (\log ^2\left (\frac {-25+e^{2+2 x}+e^{2+x} (-40-8 x)-10 x-x^2+e^2 \left (525+185 x+11 x^2-x^3\right )}{e^2 \left (25+10 x+x^2\right )}\right )\right ) \left (e^{2+2 x} (16+4 x)+e^{2+x} \left (-320-144 x-16 x^2\right )+e^2 \left (-250-150 x-30 x^2-2 x^3\right )\right ) \log \left (\frac {-25+e^{2+2 x}+e^{2+x} (-40-8 x)-10 x-x^2+e^2 \left (525+185 x+11 x^2-x^3\right )}{e^2 \left (25+10 x+x^2\right )}\right )}{-125-75 x-15 x^2-x^3+e^{2+2 x} (5+x)+e^{2+x} \left (-200-80 x-8 x^2\right )+e^2 \left (2625+1450 x+240 x^2+6 x^3-x^4\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^Log[(-25 + E^(2 + 2*x) + E^(2 + x)*(-40 - 8*x) - 10*x - x^2 + E^2*(525 + 185*x + 11*x^2 - x^3))/(E^2*(2
5 + 10*x + x^2))]^2*(E^(2 + 2*x)*(16 + 4*x) + E^(2 + x)*(-320 - 144*x - 16*x^2) + E^2*(-250 - 150*x - 30*x^2 -
 2*x^3))*Log[(-25 + E^(2 + 2*x) + E^(2 + x)*(-40 - 8*x) - 10*x - x^2 + E^2*(525 + 185*x + 11*x^2 - x^3))/(E^2*
(25 + 10*x + x^2))])/(-125 - 75*x - 15*x^2 - x^3 + E^(2 + 2*x)*(5 + x) + E^(2 + x)*(-200 - 80*x - 8*x^2) + E^2
*(2625 + 1450*x + 240*x^2 + 6*x^3 - x^4)),x]

[Out]

4*Defer[Int][E^Log[21*(1 - 1/(21*E^2)) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)]^2*Log[21*(1 - 1/(21*E^2)) -
x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)], x] + 4*Defer[Int][(E^Log[21*(1 - 1/(21*E^2)) - x + E^(2*x)/(5 + x)^2
 - (8*E^x)/(5 + x)]^2*Log[21*(1 - 1/(21*E^2)) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)])/(-5 - x), x] + 10*(8
 - 173*E^2)*Defer[Int][(E^Log[21*(1 - 1/(21*E^2)) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)]^2*Log[21*(1 - 1/(
21*E^2)) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)])/(E^(2 + 2*x) - 8*E^(2 + x)*(5 + x) - (5 + x)^2 - E^2*(-21
 + x)*(5 + x)^2), x] + 64*Defer[Int][(E^(2 + x + Log[21 - E^(-2) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)]^2)
*Log[21*(1 - 1/(21*E^2)) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)])/(E^(2 + 2*x) - 8*E^(2 + x)*(5 + x) - (5 +
 x)^2 - E^2*(-21 + x)*(5 + x)^2), x] + 12*(3 - 58*E^2)*Defer[Int][(E^Log[21*(1 - 1/(21*E^2)) - x + E^(2*x)/(5
+ x)^2 - (8*E^x)/(5 + x)]^2*x*Log[21*(1 - 1/(21*E^2)) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)])/(E^(2 + 2*x)
 - 8*E^(2 + x)*(5 + x) - (5 + x)^2 - E^2*(-21 + x)*(5 + x)^2), x] + 16*Defer[Int][(E^(2 + x + Log[21 - E^(-2)
- x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)]^2)*x*Log[21*(1 - 1/(21*E^2)) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 +
 x)])/(E^(2 + 2*x) - 8*E^(2 + x)*(5 + x) - (5 + x)^2 - E^2*(-21 + x)*(5 + x)^2), x] + 2*(2 - 25*E^2)*Defer[Int
][(E^Log[21*(1 - 1/(21*E^2)) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)]^2*x^2*Log[21*(1 - 1/(21*E^2)) - x + E^
(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)])/(E^(2 + 2*x) - 8*E^(2 + x)*(5 + x) - (5 + x)^2 - E^2*(-21 + x)*(5 + x)^2),
 x] + 4*Defer[Int][(E^(2 + Log[21 - E^(-2) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)]^2)*x^3*Log[21*(1 - 1/(21
*E^2)) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)])/(E^(2 + 2*x) - 8*E^(2 + x)*(5 + x) - (5 + x)^2 - E^2*(-21 +
 x)*(5 + x)^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \exp \left (2+\log ^2\left (21-\frac {1}{e^2}-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )\right ) \left (2 e^{2 x} (4+x)-(5+x)^3-8 e^x \left (20+9 x+x^2\right )\right ) \log \left (21 \left (1-\frac {1}{21 e^2}\right )-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )}{(5+x) \left (e^{2+2 x}-8 e^{2+x} (5+x)-(5+x)^2-e^2 (-21+x) (5+x)^2\right )} \, dx\\ &=2 \int \frac {\exp \left (2+\log ^2\left (21-\frac {1}{e^2}-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )\right ) \left (2 e^{2 x} (4+x)-(5+x)^3-8 e^x \left (20+9 x+x^2\right )\right ) \log \left (21 \left (1-\frac {1}{21 e^2}\right )-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )}{(5+x) \left (e^{2+2 x}-8 e^{2+x} (5+x)-(5+x)^2-e^2 (-21+x) (5+x)^2\right )} \, dx\\ &=2 \int \left (\frac {2 \exp \left (\log ^2\left (21-\frac {1}{e^2}-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )\right ) (4+x) \log \left (21 \left (1-\frac {1}{21 e^2}\right )-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )}{5+x}+\frac {\exp \left (\log ^2\left (21-\frac {1}{e^2}-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )\right ) \left (-32 e^{2+x}-40 \left (1-\frac {173 e^2}{8}\right )-8 e^{2+x} x-18 \left (1-\frac {58 e^2}{3}\right ) x-2 \left (1-\frac {25 e^2}{2}\right ) x^2-2 e^2 x^3\right ) \log \left (21 \left (1-\frac {1}{21 e^2}\right )-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )}{40 e^{2+x}-e^{2+2 x}+25 \left (1-21 e^2\right )+8 e^{2+x} x+10 \left (1-\frac {37 e^2}{2}\right ) x+\left (1-11 e^2\right ) x^2+e^2 x^3}\right ) \, dx\\ &=2 \int \frac {\exp \left (\log ^2\left (21-\frac {1}{e^2}-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )\right ) \left (-32 e^{2+x}-40 \left (1-\frac {173 e^2}{8}\right )-8 e^{2+x} x-18 \left (1-\frac {58 e^2}{3}\right ) x-2 \left (1-\frac {25 e^2}{2}\right ) x^2-2 e^2 x^3\right ) \log \left (21 \left (1-\frac {1}{21 e^2}\right )-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )}{40 e^{2+x}-e^{2+2 x}+25 \left (1-21 e^2\right )+8 e^{2+x} x+10 \left (1-\frac {37 e^2}{2}\right ) x+\left (1-11 e^2\right ) x^2+e^2 x^3} \, dx+4 \int \frac {\exp \left (\log ^2\left (21-\frac {1}{e^2}-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )\right ) (4+x) \log \left (21 \left (1-\frac {1}{21 e^2}\right )-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )}{5+x} \, dx\\ &=2 \int \frac {\exp \left (\log ^2\left (21 \left (1-\frac {1}{21 e^2}\right )-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )\right ) \left (8 e^{2+x} (4+x)+2 \left (20+9 x+x^2\right )+e^2 \left (-865-348 x-25 x^2+2 x^3\right )\right ) \log \left (21 \left (1-\frac {1}{21 e^2}\right )-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )}{e^{2+2 x}-8 e^{2+x} (5+x)-(5+x)^2-e^2 (-21+x) (5+x)^2} \, dx+4 \int \frac {\exp \left (\log ^2\left (21 \left (1-\frac {1}{21 e^2}\right )-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )\right ) (4+x) \log \left (21 \left (1-\frac {1}{21 e^2}\right )-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )}{5+x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.14, size = 36, normalized size = 1.29 \begin {gather*} e^{\log ^2\left (21-\frac {1}{e^2}-x+\frac {e^{2 x}}{(5+x)^2}-\frac {8 e^x}{5+x}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^Log[(-25 + E^(2 + 2*x) + E^(2 + x)*(-40 - 8*x) - 10*x - x^2 + E^2*(525 + 185*x + 11*x^2 - x^3))/(
E^2*(25 + 10*x + x^2))]^2*(E^(2 + 2*x)*(16 + 4*x) + E^(2 + x)*(-320 - 144*x - 16*x^2) + E^2*(-250 - 150*x - 30
*x^2 - 2*x^3))*Log[(-25 + E^(2 + 2*x) + E^(2 + x)*(-40 - 8*x) - 10*x - x^2 + E^2*(525 + 185*x + 11*x^2 - x^3))
/(E^2*(25 + 10*x + x^2))])/(-125 - 75*x - 15*x^2 - x^3 + E^(2 + 2*x)*(5 + x) + E^(2 + x)*(-200 - 80*x - 8*x^2)
 + E^2*(2625 + 1450*x + 240*x^2 + 6*x^3 - x^4)),x]

[Out]

E^Log[21 - E^(-2) - x + E^(2*x)/(5 + x)^2 - (8*E^x)/(5 + x)]^2

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fricas [B]  time = 0.66, size = 63, normalized size = 2.25 \begin {gather*} e^{\left (\log \left (-\frac {{\left ({\left (x^{3} - 11 \, x^{2} - 185 \, x - 525\right )} e^{4} + {\left (x^{2} + 10 \, x + 25\right )} e^{2} + 8 \, {\left (x + 5\right )} e^{\left (x + 4\right )} - e^{\left (2 \, x + 4\right )}\right )} e^{\left (-4\right )}}{x^{2} + 10 \, x + 25}\right )^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x+16)*exp(2)*exp(x)^2+(-16*x^2-144*x-320)*exp(2)*exp(x)+(-2*x^3-30*x^2-150*x-250)*exp(2))*log((e
xp(2)*exp(x)^2+(-8*x-40)*exp(2)*exp(x)+(-x^3+11*x^2+185*x+525)*exp(2)-x^2-10*x-25)/(x^2+10*x+25)/exp(2))*exp(l
og((exp(2)*exp(x)^2+(-8*x-40)*exp(2)*exp(x)+(-x^3+11*x^2+185*x+525)*exp(2)-x^2-10*x-25)/(x^2+10*x+25)/exp(2))^
2)/((5+x)*exp(2)*exp(x)^2+(-8*x^2-80*x-200)*exp(2)*exp(x)+(-x^4+6*x^3+240*x^2+1450*x+2625)*exp(2)-x^3-15*x^2-7
5*x-125),x, algorithm="fricas")

[Out]

e^(log(-((x^3 - 11*x^2 - 185*x - 525)*e^4 + (x^2 + 10*x + 25)*e^2 + 8*(x + 5)*e^(x + 4) - e^(2*x + 4))*e^(-4)/
(x^2 + 10*x + 25))^2)

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giac [B]  time = 26.02, size = 238, normalized size = 8.50 \begin {gather*} e^{\left (\log \left (-\frac {x^{3} e^{2}}{x^{2} e^{2} + 10 \, x e^{2} + 25 \, e^{2}} + \frac {11 \, x^{2} e^{2}}{x^{2} e^{2} + 10 \, x e^{2} + 25 \, e^{2}} - \frac {x^{2}}{x^{2} e^{2} + 10 \, x e^{2} + 25 \, e^{2}} + \frac {185 \, x e^{2}}{x^{2} e^{2} + 10 \, x e^{2} + 25 \, e^{2}} - \frac {8 \, x e^{\left (x + 2\right )}}{x^{2} e^{2} + 10 \, x e^{2} + 25 \, e^{2}} - \frac {10 \, x}{x^{2} e^{2} + 10 \, x e^{2} + 25 \, e^{2}} + \frac {525 \, e^{2}}{x^{2} e^{2} + 10 \, x e^{2} + 25 \, e^{2}} + \frac {e^{\left (2 \, x + 2\right )}}{x^{2} e^{2} + 10 \, x e^{2} + 25 \, e^{2}} - \frac {40 \, e^{\left (x + 2\right )}}{x^{2} e^{2} + 10 \, x e^{2} + 25 \, e^{2}} - \frac {25}{x^{2} e^{2} + 10 \, x e^{2} + 25 \, e^{2}}\right )^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x+16)*exp(2)*exp(x)^2+(-16*x^2-144*x-320)*exp(2)*exp(x)+(-2*x^3-30*x^2-150*x-250)*exp(2))*log((e
xp(2)*exp(x)^2+(-8*x-40)*exp(2)*exp(x)+(-x^3+11*x^2+185*x+525)*exp(2)-x^2-10*x-25)/(x^2+10*x+25)/exp(2))*exp(l
og((exp(2)*exp(x)^2+(-8*x-40)*exp(2)*exp(x)+(-x^3+11*x^2+185*x+525)*exp(2)-x^2-10*x-25)/(x^2+10*x+25)/exp(2))^
2)/((5+x)*exp(2)*exp(x)^2+(-8*x^2-80*x-200)*exp(2)*exp(x)+(-x^4+6*x^3+240*x^2+1450*x+2625)*exp(2)-x^3-15*x^2-7
5*x-125),x, algorithm="giac")

[Out]

e^(log(-x^3*e^2/(x^2*e^2 + 10*x*e^2 + 25*e^2) + 11*x^2*e^2/(x^2*e^2 + 10*x*e^2 + 25*e^2) - x^2/(x^2*e^2 + 10*x
*e^2 + 25*e^2) + 185*x*e^2/(x^2*e^2 + 10*x*e^2 + 25*e^2) - 8*x*e^(x + 2)/(x^2*e^2 + 10*x*e^2 + 25*e^2) - 10*x/
(x^2*e^2 + 10*x*e^2 + 25*e^2) + 525*e^2/(x^2*e^2 + 10*x*e^2 + 25*e^2) + e^(2*x + 2)/(x^2*e^2 + 10*x*e^2 + 25*e
^2) - 40*e^(x + 2)/(x^2*e^2 + 10*x*e^2 + 25*e^2) - 25/(x^2*e^2 + 10*x*e^2 + 25*e^2))^2)

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maple [C]  time = 0.75, size = 491, normalized size = 17.54




method result size



risch \({\mathrm e}^{\frac {\left (-i \pi \mathrm {csgn}\left (i \left (5+x \right )^{2}\right )^{3}+2 i \pi \mathrm {csgn}\left (i \left (5+x \right )^{2}\right )^{2} \mathrm {csgn}\left (i \left (5+x \right )\right )-i \pi \,\mathrm {csgn}\left (i \left (5+x \right )^{2}\right ) \mathrm {csgn}\left (i \left (5+x \right )\right )^{2}-i \pi \mathrm {csgn}\left (\frac {i \left (\left (x^{3}-11 x^{2}+\left (8 \,{\mathrm e}^{x}-185\right ) x -{\mathrm e}^{2 x}+40 \,{\mathrm e}^{x}-525\right ) {\mathrm e}^{2}+x^{2}+10 x +25\right )}{\left (5+x \right )^{2}}\right )^{3}-i \pi \mathrm {csgn}\left (\frac {i \left (\left (x^{3}-11 x^{2}+\left (8 \,{\mathrm e}^{x}-185\right ) x -{\mathrm e}^{2 x}+40 \,{\mathrm e}^{x}-525\right ) {\mathrm e}^{2}+x^{2}+10 x +25\right )}{\left (5+x \right )^{2}}\right )^{2} \mathrm {csgn}\left (\frac {i}{\left (5+x \right )^{2}}\right )-i \pi \mathrm {csgn}\left (\frac {i \left (\left (x^{3}-11 x^{2}+\left (8 \,{\mathrm e}^{x}-185\right ) x -{\mathrm e}^{2 x}+40 \,{\mathrm e}^{x}-525\right ) {\mathrm e}^{2}+x^{2}+10 x +25\right )}{\left (5+x \right )^{2}}\right )^{2} \mathrm {csgn}\left (i \left (\left (x^{3}-11 x^{2}+\left (8 \,{\mathrm e}^{x}-185\right ) x -{\mathrm e}^{2 x}+40 \,{\mathrm e}^{x}-525\right ) {\mathrm e}^{2}+x^{2}+10 x +25\right )\right )+i \pi \,\mathrm {csgn}\left (\frac {i \left (\left (x^{3}-11 x^{2}+\left (8 \,{\mathrm e}^{x}-185\right ) x -{\mathrm e}^{2 x}+40 \,{\mathrm e}^{x}-525\right ) {\mathrm e}^{2}+x^{2}+10 x +25\right )}{\left (5+x \right )^{2}}\right ) \mathrm {csgn}\left (\frac {i}{\left (5+x \right )^{2}}\right ) \mathrm {csgn}\left (i \left (\left (x^{3}-11 x^{2}+\left (8 \,{\mathrm e}^{x}-185\right ) x -{\mathrm e}^{2 x}+40 \,{\mathrm e}^{x}-525\right ) {\mathrm e}^{2}+x^{2}+10 x +25\right )\right )+2 i \mathrm {csgn}\left (\frac {i \left (\left (x^{3}-11 x^{2}+\left (8 \,{\mathrm e}^{x}-185\right ) x -{\mathrm e}^{2 x}+40 \,{\mathrm e}^{x}-525\right ) {\mathrm e}^{2}+x^{2}+10 x +25\right )}{\left (5+x \right )^{2}}\right )^{2} \pi -2 i \pi +4 \ln \left (5+x \right )-2 \ln \left (\left (x^{3}-11 x^{2}+\left (8 \,{\mathrm e}^{x}-185\right ) x -{\mathrm e}^{2 x}+40 \,{\mathrm e}^{x}-525\right ) {\mathrm e}^{2}+x^{2}+10 x +25\right )+4\right )^{2}}{4}}\) \(491\)



Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x+16)*exp(2)*exp(x)^2+(-16*x^2-144*x-320)*exp(2)*exp(x)+(-2*x^3-30*x^2-150*x-250)*exp(2))*ln((exp(2)*e
xp(x)^2+(-8*x-40)*exp(2)*exp(x)+(-x^3+11*x^2+185*x+525)*exp(2)-x^2-10*x-25)/(x^2+10*x+25)/exp(2))*exp(ln((exp(
2)*exp(x)^2+(-8*x-40)*exp(2)*exp(x)+(-x^3+11*x^2+185*x+525)*exp(2)-x^2-10*x-25)/(x^2+10*x+25)/exp(2))^2)/((5+x
)*exp(2)*exp(x)^2+(-8*x^2-80*x-200)*exp(2)*exp(x)+(-x^4+6*x^3+240*x^2+1450*x+2625)*exp(2)-x^3-15*x^2-75*x-125)
,x,method=_RETURNVERBOSE)

[Out]

exp(1/4*(-I*Pi*csgn(I*(5+x)^2)^3+2*I*Pi*csgn(I*(5+x)^2)^2*csgn(I*(5+x))-I*Pi*csgn(I*(5+x)^2)*csgn(I*(5+x))^2-I
*Pi*csgn(I/(5+x)^2*((x^3-11*x^2+(8*exp(x)-185)*x-exp(2*x)+40*exp(x)-525)*exp(2)+x^2+10*x+25))^3-I*Pi*csgn(I/(5
+x)^2*((x^3-11*x^2+(8*exp(x)-185)*x-exp(2*x)+40*exp(x)-525)*exp(2)+x^2+10*x+25))^2*csgn(I/(5+x)^2)-I*Pi*csgn(I
/(5+x)^2*((x^3-11*x^2+(8*exp(x)-185)*x-exp(2*x)+40*exp(x)-525)*exp(2)+x^2+10*x+25))^2*csgn(I*((x^3-11*x^2+(8*e
xp(x)-185)*x-exp(2*x)+40*exp(x)-525)*exp(2)+x^2+10*x+25))+I*Pi*csgn(I/(5+x)^2*((x^3-11*x^2+(8*exp(x)-185)*x-ex
p(2*x)+40*exp(x)-525)*exp(2)+x^2+10*x+25))*csgn(I/(5+x)^2)*csgn(I*((x^3-11*x^2+(8*exp(x)-185)*x-exp(2*x)+40*ex
p(x)-525)*exp(2)+x^2+10*x+25))+2*I*csgn(I/(5+x)^2*((x^3-11*x^2+(8*exp(x)-185)*x-exp(2*x)+40*exp(x)-525)*exp(2)
+x^2+10*x+25))^2*Pi-2*I*Pi+4*ln(5+x)-2*ln((x^3-11*x^2+(8*exp(x)-185)*x-exp(2*x)+40*exp(x)-525)*exp(2)+x^2+10*x
+25)+4)^2)

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maxima [B]  time = 1.28, size = 1199, normalized size = 42.82 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x+16)*exp(2)*exp(x)^2+(-16*x^2-144*x-320)*exp(2)*exp(x)+(-2*x^3-30*x^2-150*x-250)*exp(2))*log((e
xp(2)*exp(x)^2+(-8*x-40)*exp(2)*exp(x)+(-x^3+11*x^2+185*x+525)*exp(2)-x^2-10*x-25)/(x^2+10*x+25)/exp(2))*exp(l
og((exp(2)*exp(x)^2+(-8*x-40)*exp(2)*exp(x)+(-x^3+11*x^2+185*x+525)*exp(2)-x^2-10*x-25)/(x^2+10*x+25)/exp(2))^
2)/((5+x)*exp(2)*exp(x)^2+(-8*x^2-80*x-200)*exp(2)*exp(x)+(-x^4+6*x^3+240*x^2+1450*x+2625)*exp(2)-x^3-15*x^2-7
5*x-125),x, algorithm="maxima")

[Out]

(x^8*e^4 + 40*x^7*e^4 + 700*x^6*e^4 + 7000*x^5*e^4 + 43750*x^4*e^4 + 175000*x^3*e^4 + 437500*x^2*e^4 + 625000*
x*e^4 + 390625*e^4)*e^(log(-x^3*e^2 + x^2*(11*e^2 - 1) + 5*x*(37*e^2 - 2) - 8*(x*e^2 + 5*e^2)*e^x + 525*e^2 +
e^(2*x + 2) - 25)^2 - 4*log(-x^3*e^2 + x^2*(11*e^2 - 1) + 5*x*(37*e^2 - 2) - 8*(x*e^2 + 5*e^2)*e^x + 525*e^2 +
 e^(2*x + 2) - 25)*log(x + 5) + 4*log(x + 5)^2)/(x^12*e^8 - 4*x^11*(11*e^8 - e^6) - 2*x^10*(7*e^8 + 46*e^6 - 3
*e^4) + 4*x^9*(4249*e^8 - 497*e^6 - 3*e^4 + e^2) + x^8*(20671*e^8 + 26236*e^6 - 3234*e^4 + 76*e^2 + 1) - 40*x^
7*(78239*e^8 - 15841*e^6 + 714*e^4 + 14*e^2 - 1) - 700*x^6*(30959*e^8 - 1126*e^6 - 501*e^4 + 44*e^2 - 1) + 100
0*x^5*(167617*e^8 - 70133*e^6 + 8547*e^4 - 413*e^2 + 7) + 3125*x^4*(1002035*e^8 - 256744*e^6 + 23772*e^4 - 952
*e^2 + 14) + 12500*x^3*(1555869*e^8 - 345871*e^6 + 28524*e^4 - 1036*e^2 + 14) + 31250*x^2*(2014929*e^8 - 41592
6*e^6 + 32079*e^4 - 1096*e^2 + 14) + 312500*x*(342657*e^8 - 67473*e^6 + 4977*e^4 - 163*e^2 + 2) - 32*(x*e^8 +
5*e^8)*e^(7*x) - 4*(x^3*e^8 - x^2*(107*e^8 - e^6) - 5*x*(229*e^8 - 2*e^6) - 2925*e^8 + 25*e^6)*e^(6*x) + 32*(3
*x^4*e^8 - x^3*(82*e^8 - 3*e^6) - 15*x^2*(112*e^8 - 3*e^6) - 75*x*(122*e^8 - 3*e^6) - 15875*e^8 + 375*e^6)*e^(
5*x) + 2*(3*x^6*e^8 - 6*x^5*(75*e^8 - e^6) + x^4*(1685*e^8 - 390*e^6 + 3*e^4) + 20*x^3*(7685*e^8 - 465*e^6 + 3
*e^4) + 75*x^2*(19495*e^8 - 980*e^6 + 6*e^4) + 250*x*(21595*e^8 - 1005*e^6 + 6*e^4) + 7146875*e^8 - 318750*e^6
 + 1875*e^4)*e^(4*x) - 32*(3*x^7*e^8 - x^6*(115*e^8 - 6*e^6) - x^5*(1333*e^8 + 40*e^6 - 3*e^4) + 25*x^4*(917*e
^8 - 130*e^6 + 3*e^4) + 125*x^3*(3509*e^8 - 320*e^6 + 6*e^4) + 625*x^2*(4399*e^8 - 350*e^6 + 6*e^4) + 3125*x*(
2477*e^8 - 184*e^6 + 3*e^4) + 8334375*e^8 - 593750*e^6 + 9375*e^4)*e^(3*x) - 4*(x^9*e^8 - 3*x^8*(43*e^8 - e^6)
 + 3*x^7*(320*e^8 - 76*e^6 + e^4) + x^6*(51928*e^8 - 3060*e^6 - 69*e^4 + e^2) + 15*x^5*(4806*e^8 + 3260*e^6 -
243*e^4 + 2*e^2) - 375*x^4*(19822*e^8 - 3310*e^6 + 139*e^4 - e^2) - 625*x^3*(130808*e^8 - 16740*e^6 + 591*e^4
- 4*e^2) - 9375*x^2*(41152*e^8 - 4724*e^6 + 153*e^4 - e^2) - 9375*x*(94269*e^8 - 10180*e^6 + 313*e^4 - 2*e^2)
- 806203125*e^8 + 83671875*e^6 - 2484375*e^4 + 15625*e^2)*e^(2*x) + 32*(x^10*e^8 - x^9*(28*e^8 - 3*e^6) - 3*x^
8*(119*e^8 + 7*e^6 - e^4) + x^7*(8344*e^8 - 1512*e^6 + 42*e^4 + e^2) + 35*x^6*(3334*e^8 - 192*e^6 - 18*e^4 + e
^2) - 525*x^5*(736*e^8 - 398*e^6 + 38*e^4 - e^2) - 4375*x^4*(3566*e^8 - 738*e^6 + 48*e^4 - e^2) - 3125*x^3*(39
224*e^8 - 6720*e^6 + 378*e^4 - 7*e^2) - 9375*x^2*(49917*e^8 - 7816*e^6 + 406*e^4 - 7*e^2) - 15625*x*(58212*e^8
 - 8631*e^6 + 426*e^4 - 7*e^2) - 723515625*e^8 + 103359375*e^6 - 4921875*e^4 + 78125*e^2)*e^x + 75969140625*e^
8 - 14470312500*e^6 + 1033593750*e^4 - 32812500*e^2 + e^(8*x + 8) + 390625)

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mupad [B]  time = 6.98, size = 59, normalized size = 2.11 \begin {gather*} {\mathrm {e}}^{{\ln \left ({\mathrm {e}}^{-2}\,\left (21\,{\mathrm {e}}^2-1\right )-\frac {40\,{\mathrm {e}}^2\,{\mathrm {e}}^x-{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^2+8\,x\,{\mathrm {e}}^2\,{\mathrm {e}}^x}{{\mathrm {e}}^2\,x^2+10\,{\mathrm {e}}^2\,x+25\,{\mathrm {e}}^2}-x\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(log(-(exp(-2)*(10*x - exp(2*x)*exp(2) - exp(2)*(185*x + 11*x^2 - x^3 + 525) + x^2 + exp(2)*exp(x)*(8*
x + 40) + 25))/(10*x + x^2 + 25))^2)*log(-(exp(-2)*(10*x - exp(2*x)*exp(2) - exp(2)*(185*x + 11*x^2 - x^3 + 52
5) + x^2 + exp(2)*exp(x)*(8*x + 40) + 25))/(10*x + x^2 + 25))*(exp(2)*(150*x + 30*x^2 + 2*x^3 + 250) + exp(2)*
exp(x)*(144*x + 16*x^2 + 320) - exp(2*x)*exp(2)*(4*x + 16)))/(75*x - exp(2)*(1450*x + 240*x^2 + 6*x^3 - x^4 +
2625) + 15*x^2 + x^3 + exp(2)*exp(x)*(80*x + 8*x^2 + 200) - exp(2*x)*exp(2)*(x + 5) + 125),x)

[Out]

exp(log(exp(-2)*(21*exp(2) - 1) - (40*exp(2)*exp(x) - exp(2*x)*exp(2) + 8*x*exp(2)*exp(x))/(25*exp(2) + 10*x*e
xp(2) + x^2*exp(2)) - x)^2)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x+16)*exp(2)*exp(x)**2+(-16*x**2-144*x-320)*exp(2)*exp(x)+(-2*x**3-30*x**2-150*x-250)*exp(2))*ln
((exp(2)*exp(x)**2+(-8*x-40)*exp(2)*exp(x)+(-x**3+11*x**2+185*x+525)*exp(2)-x**2-10*x-25)/(x**2+10*x+25)/exp(2
))*exp(ln((exp(2)*exp(x)**2+(-8*x-40)*exp(2)*exp(x)+(-x**3+11*x**2+185*x+525)*exp(2)-x**2-10*x-25)/(x**2+10*x+
25)/exp(2))**2)/((5+x)*exp(2)*exp(x)**2+(-8*x**2-80*x-200)*exp(2)*exp(x)+(-x**4+6*x**3+240*x**2+1450*x+2625)*e
xp(2)-x**3-15*x**2-75*x-125),x)

[Out]

Timed out

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