3.47.100 \(\int \frac {e^{x \log ^{-\frac {2}{3 x}}(50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} (1350+180 x+6 x^2)+e^5 (-13500-2700 x-180 x^2-4 x^3))} \log ^{-1-\frac {2}{3 x}}(50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} (1350+180 x+6 x^2)+e^5 (-13500-2700 x-180 x^2-4 x^3)) (8 x+(-45 x+3 e^5 x-3 x^2) \log (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} (1350+180 x+6 x^2)+e^5 (-13500-2700 x-180 x^2-4 x^3))+(-30+2 e^5-2 x) \log (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} (1350+180 x+6 x^2)+e^5 (-13500-2700 x-180 x^2-4 x^3)) \log (\log (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} (1350+180 x+6 x^2)+e^5 (-13500-2700 x-180 x^2-4 x^3))))}{-45 x+3 e^5 x-3 x^2} \, dx\)

Optimal. Leaf size=23 \[ e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \]

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Rubi [F]  time = 4.37, 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 (x \log ^{-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right ) \log ^{-1-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \left (8 x+\left (-45 x+3 e^5 x-3 x^2\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )+\left (-30+2 e^5-2 x\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \log \left (\log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right )\right )}{-45 x+3 e^5 x-3 x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(x/Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 + x^4 + E^10*(1350 + 180*x + 6*x^2
) + E^5*(-13500 - 2700*x - 180*x^2 - 4*x^3)]^(2/(3*x)))*Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x
^2 + 60*x^3 + x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4*x^3)]^(-1 - 2/(3*x))*(8*x
+ (-45*x + 3*E^5*x - 3*x^2)*Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 + x^4 + E^10*(1
350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4*x^3)] + (-30 + 2*E^5 - 2*x)*Log[50625 + E^20 + E^15*
(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 + x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2
- 4*x^3)]*Log[Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 + x^4 + E^10*(1350 + 180*x +
6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4*x^3)]]))/(-45*x + 3*E^5*x - 3*x^2),x]

[Out]

(8*Defer[Int][(E^(x/Log[(15 - E^5 + x)^4]^(2/(3*x)))*Log[(15 - E^5 + x)^4]^(-1 - 2/(3*x)))/(-15 + E^5 - x), x]
)/3 + Defer[Int][E^(x/Log[(15 - E^5 + x)^4]^(2/(3*x)))/Log[(15 - E^5 + x)^4]^(2/(3*x)), x] + (2*Defer[Int][(E^
(x/Log[(15 - E^5 + x)^4]^(2/(3*x)))*Log[Log[(15 - E^5 + x)^4]])/(x*Log[(15 - E^5 + x)^4]^(2/(3*x))), x])/3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (x \log ^{-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right ) \log ^{-1-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \left (8 x+\left (-45 x+3 e^5 x-3 x^2\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )+\left (-30+2 e^5-2 x\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \log \left (\log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right )\right )}{\left (-45+3 e^5\right ) x-3 x^2} \, dx\\ &=\int \frac {\exp \left (x \log ^{-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right ) \log ^{-1-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \left (8 x+\left (-45 x+3 e^5 x-3 x^2\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )+\left (-30+2 e^5-2 x\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \log \left (\log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right )\right )}{\left (-45+3 e^5-3 x\right ) x} \, dx\\ &=\int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-1-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right ) \left (-8 x-\left (-15+e^5-x\right ) \log \left (\left (15-e^5+x\right )^4\right ) \left (3 x+2 \log \left (\log \left (\left (15-e^5+x\right )^4\right )\right )\right )\right )}{3 x \left (15-e^5+x\right )} \, dx\\ &=\frac {1}{3} \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-1-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right ) \left (-8 x-\left (-15+e^5-x\right ) \log \left (\left (15-e^5+x\right )^4\right ) \left (3 x+2 \log \left (\log \left (\left (15-e^5+x\right )^4\right )\right )\right )\right )}{x \left (15-e^5+x\right )} \, dx\\ &=\frac {1}{3} \int \left (\frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-1-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right ) \left (-8+45 \left (1-\frac {e^5}{15}\right ) \log \left (\left (15-e^5+x\right )^4\right )+3 x \log \left (\left (15-e^5+x\right )^4\right )\right )}{15-e^5+x}+\frac {2 e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right ) \log \left (\log \left (\left (15-e^5+x\right )^4\right )\right )}{x}\right ) \, dx\\ &=\frac {1}{3} \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-1-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right ) \left (-8+45 \left (1-\frac {e^5}{15}\right ) \log \left (\left (15-e^5+x\right )^4\right )+3 x \log \left (\left (15-e^5+x\right )^4\right )\right )}{15-e^5+x} \, dx+\frac {2}{3} \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right ) \log \left (\log \left (\left (15-e^5+x\right )^4\right )\right )}{x} \, dx\\ &=\frac {1}{3} \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-1-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right ) \left (-8-3 \left (-15+e^5-x\right ) \log \left (\left (15-e^5+x\right )^4\right )\right )}{15-e^5+x} \, dx+\frac {2}{3} \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right ) \log \left (\log \left (\left (15-e^5+x\right )^4\right )\right )}{x} \, dx\\ &=\frac {1}{3} \int \left (\frac {8 e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-1-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )}{-15+e^5-x}+3 e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )\right ) \, dx+\frac {2}{3} \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right ) \log \left (\log \left (\left (15-e^5+x\right )^4\right )\right )}{x} \, dx\\ &=\frac {2}{3} \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right ) \log \left (\log \left (\left (15-e^5+x\right )^4\right )\right )}{x} \, dx+\frac {8}{3} \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-1-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )}{-15+e^5-x} \, dx+\int e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.09, size = 23, normalized size = 1.00 \begin {gather*} e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(x/Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 + x^4 + E^10*(1350 + 180*x +
6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4*x^3)]^(2/(3*x)))*Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x +
1350*x^2 + 60*x^3 + x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4*x^3)]^(-1 - 2/(3*x)
)*(8*x + (-45*x + 3*E^5*x - 3*x^2)*Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 + x^4 + E
^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4*x^3)] + (-30 + 2*E^5 - 2*x)*Log[50625 + E^20 +
E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 + x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 1
80*x^2 - 4*x^3)]*Log[Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 + x^4 + E^10*(1350 + 18
0*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4*x^3)]]))/(-45*x + 3*E^5*x - 3*x^2),x]

[Out]

E^(x/Log[(15 - E^5 + x)^4]^(2/(3*x)))

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fricas [B]  time = 1.15, size = 68, normalized size = 2.96 \begin {gather*} e^{\left (\frac {x}{\log \left (x^{4} + 60 \, x^{3} + 1350 \, x^{2} - 4 \, {\left (x + 15\right )} e^{15} + 6 \, {\left (x^{2} + 30 \, x + 225\right )} e^{10} - 4 \, {\left (x^{3} + 45 \, x^{2} + 675 \, x + 3375\right )} e^{5} + 13500 \, x + e^{20} + 50625\right )^{\frac {2}{3 \, x}}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(5)-2*x-30)*log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*
x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625)*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(
5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))+(3*x*exp(5)-3*x^2-45*x)*log(exp(
5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+1
3500*x+50625)+8*x)*exp(x/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x
^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))/x)^2)/(3*x*exp(5)-3*x^2-45*x)/log(exp(5)^4+(-4*x-6
0)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625
)/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)
+x^4+60*x^3+1350*x^2+13500*x+50625))/x)^2,x, algorithm="fricas")

[Out]

e^(x/log(x^4 + 60*x^3 + 1350*x^2 - 4*(x + 15)*e^15 + 6*(x^2 + 30*x + 225)*e^10 - 4*(x^3 + 45*x^2 + 675*x + 337
5)*e^5 + 13500*x + e^20 + 50625)^(2/3/x))

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giac [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(((2*exp(5)-2*x-30)*log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*
x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625)*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(
5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))+(3*x*exp(5)-3*x^2-45*x)*log(exp(
5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+1
3500*x+50625)+8*x)*exp(x/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x
^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))/x)^2)/(3*x*exp(5)-3*x^2-45*x)/log(exp(5)^4+(-4*x-6
0)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625
)/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)
+x^4+60*x^3+1350*x^2+13500*x+50625))/x)^2,x, algorithm="giac")

[Out]

Timed out

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maple [F]  time = 0.21, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (2 \,{\mathrm e}^{5}-2 x -30\right ) \ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right ) \ln \left (\ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right )\right )+\left (3 x \,{\mathrm e}^{5}-3 x^{2}-45 x \right ) \ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right )+8 x \right ) {\mathrm e}^{x \,{\mathrm e}^{\frac {\ln \left (\frac {1}{\ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right )^{\frac {2}{3}}}\right )}{x}}} {\mathrm e}^{\frac {\ln \left (\frac {1}{\ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right )^{\frac {2}{3}}}\right )}{x}}}{\left (3 x \,{\mathrm e}^{5}-3 x^{2}-45 x \right ) \ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*exp(5)-2*x-30)*ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500
)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625)*ln(ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*
x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))+(3*x*exp(5)-3*x^2-45*x)*ln(exp(5)^4+(-4*x
-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+506
25)+8*x)*exp(x/exp(1/3*ln(ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13
500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))/x)^2)/(3*x*exp(5)-3*x^2-45*x)/ln(exp(5)^4+(-4*x-60)*exp(5)^3+(
6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625)/exp(1/3*ln(
ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+135
0*x^2+13500*x+50625))/x)^2,x)

[Out]

int(((2*exp(5)-2*x-30)*ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500
)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625)*ln(ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*
x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))+(3*x*exp(5)-3*x^2-45*x)*ln(exp(5)^4+(-4*x
-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+506
25)+8*x)*exp(x/exp(1/3*ln(ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13
500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))/x)^2)/(3*x*exp(5)-3*x^2-45*x)/ln(exp(5)^4+(-4*x-60)*exp(5)^3+(
6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625)/exp(1/3*ln(
ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+135
0*x^2+13500*x+50625))/x)^2,x)

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maxima [A]  time = 0.72, size = 26, normalized size = 1.13 \begin {gather*} e^{\left (x e^{\left (-\frac {4 \, \log \relax (2)}{3 \, x} - \frac {2 \, \log \left (\log \left (x - e^{5} + 15\right )\right )}{3 \, x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(5)-2*x-30)*log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*
x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625)*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(
5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))+(3*x*exp(5)-3*x^2-45*x)*log(exp(
5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+1
3500*x+50625)+8*x)*exp(x/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x
^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))/x)^2)/(3*x*exp(5)-3*x^2-45*x)/log(exp(5)^4+(-4*x-6
0)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625
)/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)
+x^4+60*x^3+1350*x^2+13500*x+50625))/x)^2,x, algorithm="maxima")

[Out]

e^(x*e^(-4/3*log(2)/x - 2/3*log(log(x - e^5 + 15))/x))

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mupad [B]  time = 4.88, size = 80, normalized size = 3.48 \begin {gather*} {\mathrm {e}}^{\frac {x}{{\ln \left (13500\,x-13500\,{\mathrm {e}}^5+1350\,{\mathrm {e}}^{10}-60\,{\mathrm {e}}^{15}+{\mathrm {e}}^{20}-2700\,x\,{\mathrm {e}}^5+180\,x\,{\mathrm {e}}^{10}-4\,x\,{\mathrm {e}}^{15}-180\,x^2\,{\mathrm {e}}^5-4\,x^3\,{\mathrm {e}}^5+6\,x^2\,{\mathrm {e}}^{10}+1350\,x^2+60\,x^3+x^4+50625\right )}^{\frac {2}{3\,x}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x*exp(-(2*log(log(13500*x + exp(20) + exp(10)*(180*x + 6*x^2 + 1350) - exp(5)*(2700*x + 180*x^2 + 4*x
^3 + 13500) + 1350*x^2 + 60*x^3 + x^4 - exp(15)*(4*x + 60) + 50625)))/(3*x)))*exp(-(2*log(log(13500*x + exp(20
) + exp(10)*(180*x + 6*x^2 + 1350) - exp(5)*(2700*x + 180*x^2 + 4*x^3 + 13500) + 1350*x^2 + 60*x^3 + x^4 - exp
(15)*(4*x + 60) + 50625)))/(3*x))*(log(13500*x + exp(20) + exp(10)*(180*x + 6*x^2 + 1350) - exp(5)*(2700*x + 1
80*x^2 + 4*x^3 + 13500) + 1350*x^2 + 60*x^3 + x^4 - exp(15)*(4*x + 60) + 50625)*(45*x - 3*x*exp(5) + 3*x^2) -
8*x + log(log(13500*x + exp(20) + exp(10)*(180*x + 6*x^2 + 1350) - exp(5)*(2700*x + 180*x^2 + 4*x^3 + 13500) +
1350*x^2 + 60*x^3 + x^4 - exp(15)*(4*x + 60) + 50625))*log(13500*x + exp(20) + exp(10)*(180*x + 6*x^2 + 1350)
- exp(5)*(2700*x + 180*x^2 + 4*x^3 + 13500) + 1350*x^2 + 60*x^3 + x^4 - exp(15)*(4*x + 60) + 50625)*(2*x - 2*
exp(5) + 30)))/(log(13500*x + exp(20) + exp(10)*(180*x + 6*x^2 + 1350) - exp(5)*(2700*x + 180*x^2 + 4*x^3 + 13
500) + 1350*x^2 + 60*x^3 + x^4 - exp(15)*(4*x + 60) + 50625)*(45*x - 3*x*exp(5) + 3*x^2)),x)

[Out]

exp(x/log(13500*x - 13500*exp(5) + 1350*exp(10) - 60*exp(15) + exp(20) - 2700*x*exp(5) + 180*x*exp(10) - 4*x*e
xp(15) - 180*x^2*exp(5) - 4*x^3*exp(5) + 6*x^2*exp(10) + 1350*x^2 + 60*x^3 + x^4 + 50625)^(2/(3*x)))

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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(((2*exp(5)-2*x-30)*ln(exp(5)**4+(-4*x-60)*exp(5)**3+(6*x**2+180*x+1350)*exp(5)**2+(-4*x**3-180*x**2-
2700*x-13500)*exp(5)+x**4+60*x**3+1350*x**2+13500*x+50625)*ln(ln(exp(5)**4+(-4*x-60)*exp(5)**3+(6*x**2+180*x+1
350)*exp(5)**2+(-4*x**3-180*x**2-2700*x-13500)*exp(5)+x**4+60*x**3+1350*x**2+13500*x+50625))+(3*x*exp(5)-3*x**
2-45*x)*ln(exp(5)**4+(-4*x-60)*exp(5)**3+(6*x**2+180*x+1350)*exp(5)**2+(-4*x**3-180*x**2-2700*x-13500)*exp(5)+
x**4+60*x**3+1350*x**2+13500*x+50625)+8*x)*exp(x/exp(1/3*ln(ln(exp(5)**4+(-4*x-60)*exp(5)**3+(6*x**2+180*x+135
0)*exp(5)**2+(-4*x**3-180*x**2-2700*x-13500)*exp(5)+x**4+60*x**3+1350*x**2+13500*x+50625))/x)**2)/(3*x*exp(5)-
3*x**2-45*x)/ln(exp(5)**4+(-4*x-60)*exp(5)**3+(6*x**2+180*x+1350)*exp(5)**2+(-4*x**3-180*x**2-2700*x-13500)*ex
p(5)+x**4+60*x**3+1350*x**2+13500*x+50625)/exp(1/3*ln(ln(exp(5)**4+(-4*x-60)*exp(5)**3+(6*x**2+180*x+1350)*exp
(5)**2+(-4*x**3-180*x**2-2700*x-13500)*exp(5)+x**4+60*x**3+1350*x**2+13500*x+50625))/x)**2,x)

[Out]

Timed out

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