3.72.76 \(\int \frac {-6625-45000 e^{2 e^{e^x}+e^x+x}-3200 x-4000 \log (3)+e^{e^{e^x}} (12000+e^{e^x+x} (22500+12000 x+15000 \log (3)))}{50625+810000 e^{4 e^{e^x}}+119250 x+99025 x^2+33920 x^3+4096 x^4+e^{3 e^{e^x}} (-1620000-864000 x-1080000 \log (3))+(135000+231000 x+123200 x^2+20480 x^3) \log (3)+(135000+149000 x+38400 x^2) \log ^2(3)+(60000+32000 x) \log ^3(3)+10000 \log ^4(3)+e^{2 e^{e^x}} (1215000+1341000 x+345600 x^2+(1620000+864000 x) \log (3)+540000 \log ^2(3))+e^{e^{e^x}} (-405000-693000 x-369600 x^2-61440 x^3+(-810000-894000 x-230400 x^2) \log (3)+(-540000-288000 x) \log ^2(3)-120000 \log ^3(3))} \, dx\)

Optimal. Leaf size=28 \[ \frac {1}{x+\left (5-2 \left (4-3 e^{e^{e^x}}+\frac {4 x}{5}+\log (3)\right )\right )^2} \]

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Rubi [F]  time = 9.41, 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 {-6625-45000 e^{2 e^{e^x}+e^x+x}-3200 x-4000 \log (3)+e^{e^{e^x}} \left (12000+e^{e^x+x} (22500+12000 x+15000 \log (3))\right )}{50625+810000 e^{4 e^{e^x}}+119250 x+99025 x^2+33920 x^3+4096 x^4+e^{3 e^{e^x}} (-1620000-864000 x-1080000 \log (3))+\left (135000+231000 x+123200 x^2+20480 x^3\right ) \log (3)+\left (135000+149000 x+38400 x^2\right ) \log ^2(3)+(60000+32000 x) \log ^3(3)+10000 \log ^4(3)+e^{2 e^{e^x}} \left (1215000+1341000 x+345600 x^2+(1620000+864000 x) \log (3)+540000 \log ^2(3)\right )+e^{e^{e^x}} \left (-405000-693000 x-369600 x^2-61440 x^3+\left (-810000-894000 x-230400 x^2\right ) \log (3)+(-540000-288000 x) \log ^2(3)-120000 \log ^3(3)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-6625 - 45000*E^(2*E^E^x + E^x + x) - 3200*x - 4000*Log[3] + E^E^E^x*(12000 + E^(E^x + x)*(22500 + 12000*
x + 15000*Log[3])))/(50625 + 810000*E^(4*E^E^x) + 119250*x + 99025*x^2 + 33920*x^3 + 4096*x^4 + E^(3*E^E^x)*(-
1620000 - 864000*x - 1080000*Log[3]) + (135000 + 231000*x + 123200*x^2 + 20480*x^3)*Log[3] + (135000 + 149000*
x + 38400*x^2)*Log[3]^2 + (60000 + 32000*x)*Log[3]^3 + 10000*Log[3]^4 + E^(2*E^E^x)*(1215000 + 1341000*x + 345
600*x^2 + (1620000 + 864000*x)*Log[3] + 540000*Log[3]^2) + E^E^E^x*(-405000 - 693000*x - 369600*x^2 - 61440*x^
3 + (-810000 - 894000*x - 230400*x^2)*Log[3] + (-540000 - 288000*x)*Log[3]^2 - 120000*Log[3]^3)),x]

[Out]

-125*(53 + 32*Log[3])*Defer[Int][(900*E^(2*E^E^x) - 480*E^E^E^x*x + 64*x^2 + 265*x*(1 + (32*Log[3])/53) - 900*
E^E^E^x*(1 + (2*Log[3])/3) + 225*(1 + (2*(3 + Log[3])*Log[9])/9))^(-2), x] + 12000*Defer[Int][E^E^E^x/(900*E^(
2*E^E^x) - 480*E^E^E^x*x + 64*x^2 + 265*x*(1 + (32*Log[3])/53) - 900*E^E^E^x*(1 + (2*Log[3])/3) + 225*(1 + (2*
(3 + Log[3])*Log[9])/9))^2, x] + 7500*(3 + Log[9])*Defer[Int][E^(E^E^x + E^x + x)/(900*E^(2*E^E^x) - 480*E^E^E
^x*x + 64*x^2 + 265*x*(1 + (32*Log[3])/53) - 900*E^E^E^x*(1 + (2*Log[3])/3) + 225*(1 + (2*(3 + Log[3])*Log[9])
/9))^2, x] - 45000*Defer[Int][E^(2*E^E^x + E^x + x)/(900*E^(2*E^E^x) - 480*E^E^E^x*x + 64*x^2 + 265*x*(1 + (32
*Log[3])/53) - 900*E^E^E^x*(1 + (2*Log[3])/3) + 225*(1 + (2*(3 + Log[3])*Log[9])/9))^2, x] - 3200*Defer[Int][x
/(900*E^(2*E^E^x) - 480*E^E^E^x*x + 64*x^2 + 265*x*(1 + (32*Log[3])/53) - 900*E^E^E^x*(1 + (2*Log[3])/3) + 225
*(1 + (2*(3 + Log[3])*Log[9])/9))^2, x] + 12000*Defer[Int][(E^(E^E^x + E^x + x)*x)/(900*E^(2*E^E^x) - 480*E^E^
E^x*x + 64*x^2 + 265*x*(1 + (32*Log[3])/53) - 900*E^E^E^x*(1 + (2*Log[3])/3) + 225*(1 + (2*(3 + Log[3])*Log[9]
)/9))^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {25 \left (480 e^{e^{e^x}}-1800 e^{2 e^{e^x}+e^x+x}-128 x-265 \left (1+\frac {32 \log (3)}{53}\right )+60 e^{e^{e^x}+e^x+x} (8 x+5 (3+\log (9)))\right )}{\left (900 e^{2 e^{e^x}}+64 x^2+5 x (53+32 \log (3))+25 (3+\log (9))^2-60 e^{e^{e^x}} (8 x+5 (3+\log (9)))\right )^2} \, dx\\ &=25 \int \frac {480 e^{e^{e^x}}-1800 e^{2 e^{e^x}+e^x+x}-128 x-265 \left (1+\frac {32 \log (3)}{53}\right )+60 e^{e^{e^x}+e^x+x} (8 x+5 (3+\log (9)))}{\left (900 e^{2 e^{e^x}}+64 x^2+5 x (53+32 \log (3))+25 (3+\log (9))^2-60 e^{e^{e^x}} (8 x+5 (3+\log (9)))\right )^2} \, dx\\ &=25 \int \left (\frac {480 e^{e^{e^x}}}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2}-\frac {128 x}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2}+\frac {60 e^{e^{e^x}+e^x+x} \left (-30 e^{e^{e^x}}+8 x+15 \left (1+\frac {2 \log (3)}{3}\right )\right )}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2}+\frac {5 (-53-32 \log (3))}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2}\right ) \, dx\\ &=1500 \int \frac {e^{e^{e^x}+e^x+x} \left (-30 e^{e^{e^x}}+8 x+15 \left (1+\frac {2 \log (3)}{3}\right )\right )}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx-3200 \int \frac {x}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx+12000 \int \frac {e^{e^{e^x}}}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx-(125 (53+32 \log (3))) \int \frac {1}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx\\ &=1500 \int \left (-\frac {30 e^{2 e^{e^x}+e^x+x}}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2}+\frac {8 e^{e^{e^x}+e^x+x} x}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2}+\frac {5 e^{e^{e^x}+e^x+x} (3+\log (9))}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2}\right ) \, dx-3200 \int \frac {x}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx+12000 \int \frac {e^{e^{e^x}}}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx-(125 (53+32 \log (3))) \int \frac {1}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx\\ &=-\left (3200 \int \frac {x}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx\right )+12000 \int \frac {e^{e^{e^x}}}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx+12000 \int \frac {e^{e^{e^x}+e^x+x} x}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx-45000 \int \frac {e^{2 e^{e^x}+e^x+x}}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx-(125 (53+32 \log (3))) \int \frac {1}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx+(7500 (3+\log (9))) \int \frac {e^{e^{e^x}+e^x+x}}{\left (900 e^{2 e^{e^x}}-480 e^{e^{e^x}} x+64 x^2+265 x \left (1+\frac {32 \log (3)}{53}\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.33, size = 57, normalized size = 2.04 \begin {gather*} \frac {25}{900 e^{2 e^{e^x}}+64 x^2+5 x (53+32 \log (3))+25 (3+\log (9))^2-60 e^{e^{e^x}} (8 x+5 (3+\log (9)))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-6625 - 45000*E^(2*E^E^x + E^x + x) - 3200*x - 4000*Log[3] + E^E^E^x*(12000 + E^(E^x + x)*(22500 +
12000*x + 15000*Log[3])))/(50625 + 810000*E^(4*E^E^x) + 119250*x + 99025*x^2 + 33920*x^3 + 4096*x^4 + E^(3*E^E
^x)*(-1620000 - 864000*x - 1080000*Log[3]) + (135000 + 231000*x + 123200*x^2 + 20480*x^3)*Log[3] + (135000 + 1
49000*x + 38400*x^2)*Log[3]^2 + (60000 + 32000*x)*Log[3]^3 + 10000*Log[3]^4 + E^(2*E^E^x)*(1215000 + 1341000*x
+ 345600*x^2 + (1620000 + 864000*x)*Log[3] + 540000*Log[3]^2) + E^E^E^x*(-405000 - 693000*x - 369600*x^2 - 61
440*x^3 + (-810000 - 894000*x - 230400*x^2)*Log[3] + (-540000 - 288000*x)*Log[3]^2 - 120000*Log[3]^3)),x]

[Out]

25/(900*E^(2*E^E^x) + 64*x^2 + 5*x*(53 + 32*Log[3]) + 25*(3 + Log[9])^2 - 60*E^E^E^x*(8*x + 5*(3 + Log[9])))

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fricas [B]  time = 0.57, size = 52, normalized size = 1.86 \begin {gather*} \frac {25}{64 \, x^{2} - 60 \, {\left (8 \, x + 10 \, \log \relax (3) + 15\right )} e^{\left (e^{\left (e^{x}\right )}\right )} + 20 \, {\left (8 \, x + 15\right )} \log \relax (3) + 100 \, \log \relax (3)^{2} + 265 \, x + 900 \, e^{\left (2 \, e^{\left (e^{x}\right )}\right )} + 225} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-45000*exp(x)*exp(exp(x))*exp(exp(exp(x)))^2+((15000*log(3)+12000*x+22500)*exp(x)*exp(exp(x))+12000
)*exp(exp(exp(x)))-4000*log(3)-3200*x-6625)/(810000*exp(exp(exp(x)))^4+(-1080000*log(3)-864000*x-1620000)*exp(
exp(exp(x)))^3+(540000*log(3)^2+(864000*x+1620000)*log(3)+345600*x^2+1341000*x+1215000)*exp(exp(exp(x)))^2+(-1
20000*log(3)^3+(-288000*x-540000)*log(3)^2+(-230400*x^2-894000*x-810000)*log(3)-61440*x^3-369600*x^2-693000*x-
405000)*exp(exp(exp(x)))+10000*log(3)^4+(32000*x+60000)*log(3)^3+(38400*x^2+149000*x+135000)*log(3)^2+(20480*x
^3+123200*x^2+231000*x+135000)*log(3)+4096*x^4+33920*x^3+99025*x^2+119250*x+50625),x, algorithm="fricas")

[Out]

25/(64*x^2 - 60*(8*x + 10*log(3) + 15)*e^(e^(e^x)) + 20*(8*x + 15)*log(3) + 100*log(3)^2 + 265*x + 900*e^(2*e^
(e^x)) + 225)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {25 \, {\left (60 \, {\left ({\left (8 \, x + 10 \, \log \relax (3) + 15\right )} e^{\left (x + e^{x}\right )} + 8\right )} e^{\left (e^{\left (e^{x}\right )}\right )} - 128 \, x - 1800 \, e^{\left (x + e^{x} + 2 \, e^{\left (e^{x}\right )}\right )} - 160 \, \log \relax (3) - 265\right )}}{4096 \, x^{4} + 4000 \, {\left (8 \, x + 15\right )} \log \relax (3)^{3} + 10000 \, \log \relax (3)^{4} + 33920 \, x^{3} + 200 \, {\left (192 \, x^{2} + 745 \, x + 675\right )} \log \relax (3)^{2} + 99025 \, x^{2} - 108000 \, {\left (8 \, x + 10 \, \log \relax (3) + 15\right )} e^{\left (3 \, e^{\left (e^{x}\right )}\right )} + 1800 \, {\left (192 \, x^{2} + 60 \, {\left (8 \, x + 15\right )} \log \relax (3) + 300 \, \log \relax (3)^{2} + 745 \, x + 675\right )} e^{\left (2 \, e^{\left (e^{x}\right )}\right )} - 120 \, {\left (512 \, x^{3} + 300 \, {\left (8 \, x + 15\right )} \log \relax (3)^{2} + 1000 \, \log \relax (3)^{3} + 3080 \, x^{2} + 10 \, {\left (192 \, x^{2} + 745 \, x + 675\right )} \log \relax (3) + 5775 \, x + 3375\right )} e^{\left (e^{\left (e^{x}\right )}\right )} + 40 \, {\left (512 \, x^{3} + 3080 \, x^{2} + 5775 \, x + 3375\right )} \log \relax (3) + 119250 \, x + 810000 \, e^{\left (4 \, e^{\left (e^{x}\right )}\right )} + 50625}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-45000*exp(x)*exp(exp(x))*exp(exp(exp(x)))^2+((15000*log(3)+12000*x+22500)*exp(x)*exp(exp(x))+12000
)*exp(exp(exp(x)))-4000*log(3)-3200*x-6625)/(810000*exp(exp(exp(x)))^4+(-1080000*log(3)-864000*x-1620000)*exp(
exp(exp(x)))^3+(540000*log(3)^2+(864000*x+1620000)*log(3)+345600*x^2+1341000*x+1215000)*exp(exp(exp(x)))^2+(-1
20000*log(3)^3+(-288000*x-540000)*log(3)^2+(-230400*x^2-894000*x-810000)*log(3)-61440*x^3-369600*x^2-693000*x-
405000)*exp(exp(exp(x)))+10000*log(3)^4+(32000*x+60000)*log(3)^3+(38400*x^2+149000*x+135000)*log(3)^2+(20480*x
^3+123200*x^2+231000*x+135000)*log(3)+4096*x^4+33920*x^3+99025*x^2+119250*x+50625),x, algorithm="giac")

[Out]

integrate(25*(60*((8*x + 10*log(3) + 15)*e^(x + e^x) + 8)*e^(e^(e^x)) - 128*x - 1800*e^(x + e^x + 2*e^(e^x)) -
160*log(3) - 265)/(4096*x^4 + 4000*(8*x + 15)*log(3)^3 + 10000*log(3)^4 + 33920*x^3 + 200*(192*x^2 + 745*x +
675)*log(3)^2 + 99025*x^2 - 108000*(8*x + 10*log(3) + 15)*e^(3*e^(e^x)) + 1800*(192*x^2 + 60*(8*x + 15)*log(3)
+ 300*log(3)^2 + 745*x + 675)*e^(2*e^(e^x)) - 120*(512*x^3 + 300*(8*x + 15)*log(3)^2 + 1000*log(3)^3 + 3080*x
^2 + 10*(192*x^2 + 745*x + 675)*log(3) + 5775*x + 3375)*e^(e^(e^x)) + 40*(512*x^3 + 3080*x^2 + 5775*x + 3375)*
log(3) + 119250*x + 810000*e^(4*e^(e^x)) + 50625), x)

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maple [B]  time = 0.08, size = 59, normalized size = 2.11

method	result	size
risch	\(\frac {25}{100 \ln \relax (3)^{2}-600 \ln \relax (3) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+160 x \ln \relax (3)+900 \,{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{x}}}-480 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}} x +64 x^{2}+300 \ln \relax (3)-900 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+265 x +225}\)	\(59\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-45000*exp(x)*exp(exp(x))*exp(exp(exp(x)))^2+((15000*ln(3)+12000*x+22500)*exp(x)*exp(exp(x))+12000)*exp(e
xp(exp(x)))-4000*ln(3)-3200*x-6625)/(810000*exp(exp(exp(x)))^4+(-1080000*ln(3)-864000*x-1620000)*exp(exp(exp(x
)))^3+(540000*ln(3)^2+(864000*x+1620000)*ln(3)+345600*x^2+1341000*x+1215000)*exp(exp(exp(x)))^2+(-120000*ln(3)
^3+(-288000*x-540000)*ln(3)^2+(-230400*x^2-894000*x-810000)*ln(3)-61440*x^3-369600*x^2-693000*x-405000)*exp(ex
p(exp(x)))+10000*ln(3)^4+(32000*x+60000)*ln(3)^3+(38400*x^2+149000*x+135000)*ln(3)^2+(20480*x^3+123200*x^2+231
000*x+135000)*ln(3)+4096*x^4+33920*x^3+99025*x^2+119250*x+50625),x,method=_RETURNVERBOSE)

[Out]

25/(100*ln(3)^2-600*ln(3)*exp(exp(exp(x)))+160*x*ln(3)+900*exp(2*exp(exp(x)))-480*exp(exp(exp(x)))*x+64*x^2+30
0*ln(3)-900*exp(exp(exp(x)))+265*x+225)

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maxima [B]  time = 0.82, size = 53, normalized size = 1.89 \begin {gather*} \frac {25}{64 \, x^{2} + 5 \, x {\left (32 \, \log \relax (3) + 53\right )} - 60 \, {\left (8 \, x + 10 \, \log \relax (3) + 15\right )} e^{\left (e^{\left (e^{x}\right )}\right )} + 100 \, \log \relax (3)^{2} + 900 \, e^{\left (2 \, e^{\left (e^{x}\right )}\right )} + 300 \, \log \relax (3) + 225} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-45000*exp(x)*exp(exp(x))*exp(exp(exp(x)))^2+((15000*log(3)+12000*x+22500)*exp(x)*exp(exp(x))+12000
)*exp(exp(exp(x)))-4000*log(3)-3200*x-6625)/(810000*exp(exp(exp(x)))^4+(-1080000*log(3)-864000*x-1620000)*exp(
exp(exp(x)))^3+(540000*log(3)^2+(864000*x+1620000)*log(3)+345600*x^2+1341000*x+1215000)*exp(exp(exp(x)))^2+(-1
20000*log(3)^3+(-288000*x-540000)*log(3)^2+(-230400*x^2-894000*x-810000)*log(3)-61440*x^3-369600*x^2-693000*x-
405000)*exp(exp(exp(x)))+10000*log(3)^4+(32000*x+60000)*log(3)^3+(38400*x^2+149000*x+135000)*log(3)^2+(20480*x
^3+123200*x^2+231000*x+135000)*log(3)+4096*x^4+33920*x^3+99025*x^2+119250*x+50625),x, algorithm="maxima")

[Out]

25/(64*x^2 + 5*x*(32*log(3) + 53) - 60*(8*x + 10*log(3) + 15)*e^(e^(e^x)) + 100*log(3)^2 + 900*e^(2*e^(e^x)) +
300*log(3) + 225)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {3200\,x+4000\,\ln \relax (3)-{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}\,\left ({\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^x\,\left (12000\,x+15000\,\ln \relax (3)+22500\right )+12000\right )+45000\,{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^x+6625}{119250\,x+810000\,{\mathrm {e}}^{4\,{\mathrm {e}}^{{\mathrm {e}}^x}}+{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,\left (1341000\,x+\ln \relax (3)\,\left (864000\,x+1620000\right )+540000\,{\ln \relax (3)}^2+345600\,x^2+1215000\right )+{\ln \relax (3)}^3\,\left (32000\,x+60000\right )-{\mathrm {e}}^{3\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,\left (864000\,x+1080000\,\ln \relax (3)+1620000\right )+\ln \relax (3)\,\left (20480\,x^3+123200\,x^2+231000\,x+135000\right )-{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}\,\left (693000\,x+\ln \relax (3)\,\left (230400\,x^2+894000\,x+810000\right )+{\ln \relax (3)}^2\,\left (288000\,x+540000\right )+120000\,{\ln \relax (3)}^3+369600\,x^2+61440\,x^3+405000\right )+{\ln \relax (3)}^2\,\left (38400\,x^2+149000\,x+135000\right )+10000\,{\ln \relax (3)}^4+99025\,x^2+33920\,x^3+4096\,x^4+50625} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3200*x + 4000*log(3) - exp(exp(exp(x)))*(exp(exp(x))*exp(x)*(12000*x + 15000*log(3) + 22500) + 12000) +
45000*exp(2*exp(exp(x)))*exp(exp(x))*exp(x) + 6625)/(119250*x + 810000*exp(4*exp(exp(x))) + exp(2*exp(exp(x)))
*(1341000*x + log(3)*(864000*x + 1620000) + 540000*log(3)^2 + 345600*x^2 + 1215000) + log(3)^3*(32000*x + 6000
0) - exp(3*exp(exp(x)))*(864000*x + 1080000*log(3) + 1620000) + log(3)*(231000*x + 123200*x^2 + 20480*x^3 + 13
5000) - exp(exp(exp(x)))*(693000*x + log(3)*(894000*x + 230400*x^2 + 810000) + log(3)^2*(288000*x + 540000) +
120000*log(3)^3 + 369600*x^2 + 61440*x^3 + 405000) + log(3)^2*(149000*x + 38400*x^2 + 135000) + 10000*log(3)^4
+ 99025*x^2 + 33920*x^3 + 4096*x^4 + 50625),x)

[Out]

int(-(3200*x + 4000*log(3) - exp(exp(exp(x)))*(exp(exp(x))*exp(x)*(12000*x + 15000*log(3) + 22500) + 12000) +
45000*exp(2*exp(exp(x)))*exp(exp(x))*exp(x) + 6625)/(119250*x + 810000*exp(4*exp(exp(x))) + exp(2*exp(exp(x)))
*(1341000*x + log(3)*(864000*x + 1620000) + 540000*log(3)^2 + 345600*x^2 + 1215000) + log(3)^3*(32000*x + 6000
0) - exp(3*exp(exp(x)))*(864000*x + 1080000*log(3) + 1620000) + log(3)*(231000*x + 123200*x^2 + 20480*x^3 + 13
5000) - exp(exp(exp(x)))*(693000*x + log(3)*(894000*x + 230400*x^2 + 810000) + log(3)^2*(288000*x + 540000) +
120000*log(3)^3 + 369600*x^2 + 61440*x^3 + 405000) + log(3)^2*(149000*x + 38400*x^2 + 135000) + 10000*log(3)^4
+ 99025*x^2 + 33920*x^3 + 4096*x^4 + 50625), x)

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sympy [B]  time = 0.51, size = 58, normalized size = 2.07 \begin {gather*} \frac {25}{64 x^{2} + 160 x \log {\relax (3 )} + 265 x + \left (- 480 x - 900 - 600 \log {\relax (3 )}\right ) e^{e^{e^{x}}} + 900 e^{2 e^{e^{x}}} + 100 \log {\relax (3 )}^{2} + 225 + 300 \log {\relax (3 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-45000*exp(x)*exp(exp(x))*exp(exp(exp(x)))**2+((15000*ln(3)+12000*x+22500)*exp(x)*exp(exp(x))+12000
)*exp(exp(exp(x)))-4000*ln(3)-3200*x-6625)/(810000*exp(exp(exp(x)))**4+(-1080000*ln(3)-864000*x-1620000)*exp(e
xp(exp(x)))**3+(540000*ln(3)**2+(864000*x+1620000)*ln(3)+345600*x**2+1341000*x+1215000)*exp(exp(exp(x)))**2+(-
120000*ln(3)**3+(-288000*x-540000)*ln(3)**2+(-230400*x**2-894000*x-810000)*ln(3)-61440*x**3-369600*x**2-693000
*x-405000)*exp(exp(exp(x)))+10000*ln(3)**4+(32000*x+60000)*ln(3)**3+(38400*x**2+149000*x+135000)*ln(3)**2+(204
80*x**3+123200*x**2+231000*x+135000)*ln(3)+4096*x**4+33920*x**3+99025*x**2+119250*x+50625),x)

[Out]

25/(64*x**2 + 160*x*log(3) + 265*x + (-480*x - 900 - 600*log(3))*exp(exp(exp(x))) + 900*exp(2*exp(exp(x))) + 1
00*log(3)**2 + 225 + 300*log(3))

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