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3.94.36 \(\int \frac {e^x (-4050 x-2025 x^2+81 x^3+(-2025-2106 x+81 x^2) \log (5))+e^{2+e^x} (e^{2 x} (2700 x^2-108 x^3+(2700 x-108 x^2) \log (5))+e^x (5400 x+2700 x^2-108 x^3+(2700+2808 x-108 x^2) \log (5)))+e^{6+3 e^x} (e^{2 x} (900 x^2-36 x^3+(900 x-36 x^2) \log (5))+e^x (600 x+300 x^2-12 x^3+(300+312 x-12 x^2) \log (5)))+e^{8+4 e^x} (e^x (-50 x-25 x^2+x^3+(-25-26 x+x^2) \log (5))+e^{2 x} (-100 x^2+4 x^3+(-100 x+4 x^2) \log (5)))+e^{4+2 e^x} (e^x (-2700 x-1350 x^2+54 x^3+(-1350-1404 x+54 x^2) \log (5))+e^{2 x} (-2700 x^2+108 x^3+(-2700 x+108 x^2) \log (5)))}{-15625+1875 x-75 x^2+x^3} \, dx\)

Optimal. Leaf size=29 \[ \frac {e^x \left (3-e^{2+e^x}\right )^4 x (x+\log (5))}{(25-x)^2} \]

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Rubi [F]  time = 19.06, 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 {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^x*(-4050*x - 2025*x^2 + 81*x^3 + (-2025 - 2106*x + 81*x^2)*Log[5]) + E^(2 + E^x)*(E^(2*x)*(2700*x^2 - 1
08*x^3 + (2700*x - 108*x^2)*Log[5]) + E^x*(5400*x + 2700*x^2 - 108*x^3 + (2700 + 2808*x - 108*x^2)*Log[5])) +
E^(6 + 3*E^x)*(E^(2*x)*(900*x^2 - 36*x^3 + (900*x - 36*x^2)*Log[5]) + E^x*(600*x + 300*x^2 - 12*x^3 + (300 + 3
12*x - 12*x^2)*Log[5])) + E^(8 + 4*E^x)*(E^x*(-50*x - 25*x^2 + x^3 + (-25 - 26*x + x^2)*Log[5]) + E^(2*x)*(-10
0*x^2 + 4*x^3 + (-100*x + 4*x^2)*Log[5])) + E^(4 + 2*E^x)*(E^x*(-2700*x - 1350*x^2 + 54*x^3 + (-1350 - 1404*x
+ 54*x^2)*Log[5]) + E^(2*x)*(-2700*x^2 + 108*x^3 + (-2700*x + 108*x^2)*Log[5])))/(-15625 + 1875*x - 75*x^2 + x
^3),x]

[Out]

27*E^(4 + 2*E^x) + E^(8 + 4*E^x)/4 + 81*E^x - 108*E^(2 + E^x + x) - 12*E^(6 + 3*E^x + x) - (1265625*E^x)/(2*(2
5 - x)^2) + (1569375*E^x)/(2*(25 - x)) + (1581525*E^25*ExpIntegralEi[-25 + x])/2 + (50625*E^x*(25 - Log[5]))/(
2*(25 - x)^2) - (58725*E^x*(25 - Log[5]))/(2*(25 - x)) - (58887*E^25*ExpIntegralEi[-25 + x]*(25 - Log[5]))/2 +
 (2025*E^x*Log[5])/(2*(25 - x)^2) - (2025*E^x*Log[5])/(2*(25 - x)) - (2025*E^25*ExpIntegralEi[-25 + x]*Log[5])
/2 + (2025*E^x*(25 + 13*Log[5]))/(25 - x)^2 - (2187*E^x*(25 + 13*Log[5]))/(25 - x) - 2187*E^25*ExpIntegralEi[-
25 + x]*(25 + 13*Log[5]) + 108*Defer[Int][E^(2*(2 + E^x + x)), x] + 4*Defer[Int][E^(2*(4 + 2*E^x + x)), x] - 3
00*Log[5]*Defer[Int][E^(3*(2 + E^x) + x)/(25 - x)^3, x] - 9*(25 - Log[5])*Defer[Int][E^(6 + 3*E^x + x)/(25 - x
), x] + 27*(25 - Log[5])*Defer[Int][E^(2*(2 + E^x) + x)/(25 - x), x] - 1687500*Defer[Int][E^(2 + E^x + x)/(-25
 + x)^3, x] + 67500*(25 - Log[5])*Defer[Int][E^(2 + E^x + x)/(-25 + x)^3, x] + 2700*Log[5]*Defer[Int][E^(2 + E
^x + x)/(-25 + x)^3, x] + 5400*(25 + 13*Log[5])*Defer[Int][E^(2 + E^x + x)/(-25 + x)^3, x] + 421875*Defer[Int]
[E^(4 + 2*E^x + x)/(-25 + x)^3, x] - 16875*(25 - Log[5])*Defer[Int][E^(4 + 2*E^x + x)/(-25 + x)^3, x] - 1350*(
25 + 13*Log[5])*Defer[Int][E^(4 + 2*E^x + x)/(-25 + x)^3, x] - 140625*Defer[Int][E^(6 + 3*E^x + x)/(-25 + x)^3
, x] + 5625*(25 - Log[5])*Defer[Int][E^(6 + 3*E^x + x)/(-25 + x)^3, x] + 450*(25 + 13*Log[5])*Defer[Int][E^(6
+ 3*E^x + x)/(-25 + x)^3, x] + 15625*Defer[Int][E^(8 + 4*E^x + x)/(-25 + x)^3, x] - 625*(25 - Log[5])*Defer[In
t][E^(8 + 4*E^x + x)/(-25 + x)^3, x] - 50*(25 + 13*Log[5])*Defer[Int][E^(8 + 4*E^x + x)/(-25 + x)^3, x] + 4218
75*Defer[Int][E^(2*(2 + E^x) + x)/(-25 + x)^3, x] - 16875*(25 - Log[5])*Defer[Int][E^(2*(2 + E^x) + x)/(-25 +
x)^3, x] - 1350*Log[5]*Defer[Int][E^(2*(2 + E^x) + x)/(-25 + x)^3, x] - 1350*(25 + 13*Log[5])*Defer[Int][E^(2*
(2 + E^x) + x)/(-25 + x)^3, x] - 46875*Defer[Int][E^(3*(2 + E^x) + x)/(-25 + x)^3, x] + 1875*(25 - Log[5])*Def
er[Int][E^(3*(2 + E^x) + x)/(-25 + x)^3, x] + 150*(25 + 13*Log[5])*Defer[Int][E^(3*(2 + E^x) + x)/(-25 + x)^3,
 x] - 25*Log[5]*Defer[Int][E^(4*(2 + E^x) + x)/(-25 + x)^3, x] - 202500*Defer[Int][E^(2 + E^x + x)/(-25 + x)^2
, x] + 5400*(25 - Log[5])*Defer[Int][E^(2 + E^x + x)/(-25 + x)^2, x] + 216*(25 + 13*Log[5])*Defer[Int][E^(2 +
E^x + x)/(-25 + x)^2, x] + 2700*(25 + Log[5])*Defer[Int][E^(2*(2 + E^x + x))/(-25 + x)^2, x] + 50625*Defer[Int
][E^(4 + 2*E^x + x)/(-25 + x)^2, x] - 1350*(25 - Log[5])*Defer[Int][E^(4 + 2*E^x + x)/(-25 + x)^2, x] - 54*(25
 + 13*Log[5])*Defer[Int][E^(4 + 2*E^x + x)/(-25 + x)^2, x] + 100*(25 + Log[5])*Defer[Int][E^(2*(4 + 2*E^x + x)
)/(-25 + x)^2, x] - 16875*Defer[Int][E^(6 + 3*E^x + x)/(-25 + x)^2, x] + 450*(25 - Log[5])*Defer[Int][E^(6 + 3
*E^x + x)/(-25 + x)^2, x] + 18*(25 + 13*Log[5])*Defer[Int][E^(6 + 3*E^x + x)/(-25 + x)^2, x] + 1875*Defer[Int]
[E^(8 + 4*E^x + x)/(-25 + x)^2, x] - 50*(25 - Log[5])*Defer[Int][E^(8 + 4*E^x + x)/(-25 + x)^2, x] - 2*(25 + 1
3*Log[5])*Defer[Int][E^(8 + 4*E^x + x)/(-25 + x)^2, x] + 50625*Defer[Int][E^(2*(2 + E^x) + x)/(-25 + x)^2, x]
- 1350*(25 - Log[5])*Defer[Int][E^(2*(2 + E^x) + x)/(-25 + x)^2, x] - 54*(25 + 13*Log[5])*Defer[Int][E^(2*(2 +
 E^x) + x)/(-25 + x)^2, x] - 5625*Defer[Int][E^(3*(2 + E^x) + x)/(-25 + x)^2, x] + 150*(25 - Log[5])*Defer[Int
][E^(3*(2 + E^x) + x)/(-25 + x)^2, x] + 6*(25 + 13*Log[5])*Defer[Int][E^(3*(2 + E^x) + x)/(-25 + x)^2, x] - 27
00*(25 + Log[5])*Defer[Int][E^(2 + E^x + 2*x)/(-25 + x)^2, x] - 900*(25 + Log[5])*Defer[Int][E^(6 + 3*E^x + 2*
x)/(-25 + x)^2, x] - 8100*Defer[Int][E^(2 + E^x + x)/(-25 + x), x] + 108*(25 - Log[5])*Defer[Int][E^(2 + E^x +
 x)/(-25 + x), x] + 108*(50 + Log[5])*Defer[Int][E^(2*(2 + E^x + x))/(-25 + x), x] + 2025*Defer[Int][E^(4 + 2*
E^x + x)/(-25 + x), x] - 27*(25 - Log[5])*Defer[Int][E^(4 + 2*E^x + x)/(-25 + x), x] + 4*(50 + Log[5])*Defer[I
nt][E^(2*(4 + 2*E^x + x))/(-25 + x), x] - 675*Defer[Int][E^(6 + 3*E^x + x)/(-25 + x), x] + 75*Defer[Int][E^(8
+ 4*E^x + x)/(-25 + x), x] - (25 - Log[5])*Defer[Int][E^(8 + 4*E^x + x)/(-25 + x), x] + 2025*Defer[Int][E^(2*(
2 + E^x) + x)/(-25 + x), x] - 225*Defer[Int][E^(3*(2 + E^x) + x)/(-25 + x), x] + 3*(25 - Log[5])*Defer[Int][E^
(3*(2 + E^x) + x)/(-25 + x), x] - 108*(50 + Log[5])*Defer[Int][E^(2 + E^x + 2*x)/(-25 + x), x] - 36*(50 + Log[
5])*Defer[Int][E^(6 + 3*E^x + 2*x)/(-25 + x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x \left (3-e^{2+e^x}\right )^3 \left (\left (-3+e^{2+e^x}+4 e^{2+e^x+x}\right ) x^3+\left (-3+e^{2+e^x}+4 e^{2+e^x+x}\right ) x^2 (-25+\log (5))-25 \left (-3+e^{2+e^x}\right ) \log (5)-2 x \left (-75-39 \log (5)+50 e^{2+e^x+x} \log (5)+e^{2+e^x} (25+13 \log (5))\right )\right )}{(25-x)^3} \, dx\\ &=\int \left (-\frac {3 e^x \left (-3+e^{2+e^x}\right )^3 x^3}{(-25+x)^3}+\frac {e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x^3}{(-25+x)^3}+\frac {150 e^x \left (-3+e^{2+e^x}\right )^3 x \left (1+\frac {13 \log (5)}{25}\right )}{(-25+x)^3}-\frac {3 e^x \left (-3+e^{2+e^x}\right )^3 x^2 (-25+\log (5))}{(-25+x)^3}+\frac {e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x^2 (-25+\log (5))}{(-25+x)^3}-\frac {25 e^x \left (-3+e^{2+e^x}\right )^4 \log (5)}{(-25+x)^3}+\frac {4 e^{2+e^x+2 x} \left (-3+e^{2+e^x}\right )^3 x (x+\log (5))}{(-25+x)^2}-\frac {2 e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x (25+13 \log (5))}{(-25+x)^3}\right ) \, dx\\ &=-\left (3 \int \frac {e^x \left (-3+e^{2+e^x}\right )^3 x^3}{(-25+x)^3} \, dx\right )+4 \int \frac {e^{2+e^x+2 x} \left (-3+e^{2+e^x}\right )^3 x (x+\log (5))}{(-25+x)^2} \, dx+(-25+\log (5)) \int \frac {e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x^2}{(-25+x)^3} \, dx-(3 (-25+\log (5))) \int \frac {e^x \left (-3+e^{2+e^x}\right )^3 x^2}{(-25+x)^3} \, dx-(25 \log (5)) \int \frac {e^x \left (-3+e^{2+e^x}\right )^4}{(-25+x)^3} \, dx-(2 (25+13 \log (5))) \int \frac {e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x}{(-25+x)^3} \, dx+(6 (25+13 \log (5))) \int \frac {e^x \left (-3+e^{2+e^x}\right )^3 x}{(-25+x)^3} \, dx+\int \frac {e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x^3}{(-25+x)^3} \, dx\\ &=-\left (3 \int \left (\frac {9 e^{2 \left (2+e^x\right )+x} x^3}{(25-x)^3}-\frac {27 e^x x^3}{(-25+x)^3}+\frac {27 e^{2+e^x+x} x^3}{(-25+x)^3}+\frac {e^{3 \left (2+e^x\right )+x} x^3}{(-25+x)^3}\right ) \, dx\right )+4 \int \left (\frac {9 e^{2+e^x+2 \left (2+e^x\right )+2 x} x (-x-\log (5))}{(25-x)^2}+\frac {e^{2+e^x+3 \left (2+e^x\right )+2 x} x (x+\log (5))}{(25-x)^2}-\frac {27 e^{2+e^x+2 x} x (x+\log (5))}{(-25+x)^2}+\frac {27 e^{4+2 e^x+2 x} x (x+\log (5))}{(-25+x)^2}\right ) \, dx+(-25+\log (5)) \int \left (\frac {9 e^{2+e^x+2 \left (2+e^x\right )+x} x^2}{(25-x)^3}-\frac {27 e^{2+e^x+x} x^2}{(-25+x)^3}+\frac {27 e^{4+2 e^x+x} x^2}{(-25+x)^3}+\frac {e^{2+e^x+3 \left (2+e^x\right )+x} x^2}{(-25+x)^3}\right ) \, dx-(3 (-25+\log (5))) \int \left (\frac {9 e^{2 \left (2+e^x\right )+x} x^2}{(25-x)^3}-\frac {27 e^x x^2}{(-25+x)^3}+\frac {27 e^{2+e^x+x} x^2}{(-25+x)^3}+\frac {e^{3 \left (2+e^x\right )+x} x^2}{(-25+x)^3}\right ) \, dx-(25 \log (5)) \int \left (\frac {12 e^{3 \left (2+e^x\right )+x}}{(25-x)^3}+\frac {81 e^x}{(-25+x)^3}-\frac {108 e^{2+e^x+x}}{(-25+x)^3}+\frac {54 e^{2 \left (2+e^x\right )+x}}{(-25+x)^3}+\frac {e^{4 \left (2+e^x\right )+x}}{(-25+x)^3}\right ) \, dx-(2 (25+13 \log (5))) \int \left (\frac {9 e^{2+e^x+2 \left (2+e^x\right )+x} x}{(25-x)^3}-\frac {27 e^{2+e^x+x} x}{(-25+x)^3}+\frac {27 e^{4+2 e^x+x} x}{(-25+x)^3}+\frac {e^{2+e^x+3 \left (2+e^x\right )+x} x}{(-25+x)^3}\right ) \, dx+(6 (25+13 \log (5))) \int \left (\frac {9 e^{2 \left (2+e^x\right )+x} x}{(25-x)^3}-\frac {27 e^x x}{(-25+x)^3}+\frac {27 e^{2+e^x+x} x}{(-25+x)^3}+\frac {e^{3 \left (2+e^x\right )+x} x}{(-25+x)^3}\right ) \, dx+\int \left (\frac {9 e^{2+e^x+2 \left (2+e^x\right )+x} x^3}{(25-x)^3}-\frac {27 e^{2+e^x+x} x^3}{(-25+x)^3}+\frac {27 e^{4+2 e^x+x} x^3}{(-25+x)^3}+\frac {e^{2+e^x+3 \left (2+e^x\right )+x} x^3}{(-25+x)^3}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.33, size = 25, normalized size = 0.86 \begin {gather*} \frac {e^x \left (-3+e^{2+e^x}\right )^4 x (x+\log (5))}{(-25+x)^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^x*(-4050*x - 2025*x^2 + 81*x^3 + (-2025 - 2106*x + 81*x^2)*Log[5]) + E^(2 + E^x)*(E^(2*x)*(2700*x
^2 - 108*x^3 + (2700*x - 108*x^2)*Log[5]) + E^x*(5400*x + 2700*x^2 - 108*x^3 + (2700 + 2808*x - 108*x^2)*Log[5
])) + E^(6 + 3*E^x)*(E^(2*x)*(900*x^2 - 36*x^3 + (900*x - 36*x^2)*Log[5]) + E^x*(600*x + 300*x^2 - 12*x^3 + (3
00 + 312*x - 12*x^2)*Log[5])) + E^(8 + 4*E^x)*(E^x*(-50*x - 25*x^2 + x^3 + (-25 - 26*x + x^2)*Log[5]) + E^(2*x
)*(-100*x^2 + 4*x^3 + (-100*x + 4*x^2)*Log[5])) + E^(4 + 2*E^x)*(E^x*(-2700*x - 1350*x^2 + 54*x^3 + (-1350 - 1
404*x + 54*x^2)*Log[5]) + E^(2*x)*(-2700*x^2 + 108*x^3 + (-2700*x + 108*x^2)*Log[5])))/(-15625 + 1875*x - 75*x
^2 + x^3),x]

[Out]

(E^x*(-3 + E^(2 + E^x))^4*x*(x + Log[5]))/(-25 + x)^2

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fricas [B]  time = 0.64, size = 93, normalized size = 3.21 \begin {gather*} \frac {{\left (x^{2} + x \log \relax (5)\right )} e^{\left (x + 4 \, e^{x} + 8\right )} - 12 \, {\left (x^{2} + x \log \relax (5)\right )} e^{\left (x + 3 \, e^{x} + 6\right )} + 54 \, {\left (x^{2} + x \log \relax (5)\right )} e^{\left (x + 2 \, e^{x} + 4\right )} - 108 \, {\left (x^{2} + x \log \relax (5)\right )} e^{\left (x + e^{x} + 2\right )} + 81 \, {\left (x^{2} + x \log \relax (5)\right )} e^{x}}{x^{2} - 50 \, x + 625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4*x^2-100*x)*log(5)+4*x^3-100*x^2)*exp(x)^2+((x^2-26*x-25)*log(5)+x^3-25*x^2-50*x)*exp(x))*exp(e
xp(x)+2)^4+(((-36*x^2+900*x)*log(5)-36*x^3+900*x^2)*exp(x)^2+((-12*x^2+312*x+300)*log(5)-12*x^3+300*x^2+600*x)
*exp(x))*exp(exp(x)+2)^3+(((108*x^2-2700*x)*log(5)+108*x^3-2700*x^2)*exp(x)^2+((54*x^2-1404*x-1350)*log(5)+54*
x^3-1350*x^2-2700*x)*exp(x))*exp(exp(x)+2)^2+(((-108*x^2+2700*x)*log(5)-108*x^3+2700*x^2)*exp(x)^2+((-108*x^2+
2808*x+2700)*log(5)-108*x^3+2700*x^2+5400*x)*exp(x))*exp(exp(x)+2)+((81*x^2-2106*x-2025)*log(5)+81*x^3-2025*x^
2-4050*x)*exp(x))/(x^3-75*x^2+1875*x-15625),x, algorithm="fricas")

[Out]

((x^2 + x*log(5))*e^(x + 4*e^x + 8) - 12*(x^2 + x*log(5))*e^(x + 3*e^x + 6) + 54*(x^2 + x*log(5))*e^(x + 2*e^x
 + 4) - 108*(x^2 + x*log(5))*e^(x + e^x + 2) + 81*(x^2 + x*log(5))*e^x)/(x^2 - 50*x + 625)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {81 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \relax (5) - 50 \, x\right )} e^{x} + {\left (4 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \relax (5)\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \relax (5) - 50 \, x\right )} e^{x}\right )} e^{\left (4 \, e^{x} + 8\right )} - 12 \, {\left (3 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \relax (5)\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \relax (5) - 50 \, x\right )} e^{x}\right )} e^{\left (3 \, e^{x} + 6\right )} + 54 \, {\left (2 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \relax (5)\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \relax (5) - 50 \, x\right )} e^{x}\right )} e^{\left (2 \, e^{x} + 4\right )} - 108 \, {\left ({\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \relax (5)\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \relax (5) - 50 \, x\right )} e^{x}\right )} e^{\left (e^{x} + 2\right )}}{x^{3} - 75 \, x^{2} + 1875 \, x - 15625}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4*x^2-100*x)*log(5)+4*x^3-100*x^2)*exp(x)^2+((x^2-26*x-25)*log(5)+x^3-25*x^2-50*x)*exp(x))*exp(e
xp(x)+2)^4+(((-36*x^2+900*x)*log(5)-36*x^3+900*x^2)*exp(x)^2+((-12*x^2+312*x+300)*log(5)-12*x^3+300*x^2+600*x)
*exp(x))*exp(exp(x)+2)^3+(((108*x^2-2700*x)*log(5)+108*x^3-2700*x^2)*exp(x)^2+((54*x^2-1404*x-1350)*log(5)+54*
x^3-1350*x^2-2700*x)*exp(x))*exp(exp(x)+2)^2+(((-108*x^2+2700*x)*log(5)-108*x^3+2700*x^2)*exp(x)^2+((-108*x^2+
2808*x+2700)*log(5)-108*x^3+2700*x^2+5400*x)*exp(x))*exp(exp(x)+2)+((81*x^2-2106*x-2025)*log(5)+81*x^3-2025*x^
2-4050*x)*exp(x))/(x^3-75*x^2+1875*x-15625),x, algorithm="giac")

[Out]

integrate((81*(x^3 - 25*x^2 + (x^2 - 26*x - 25)*log(5) - 50*x)*e^x + (4*(x^3 - 25*x^2 + (x^2 - 25*x)*log(5))*e
^(2*x) + (x^3 - 25*x^2 + (x^2 - 26*x - 25)*log(5) - 50*x)*e^x)*e^(4*e^x + 8) - 12*(3*(x^3 - 25*x^2 + (x^2 - 25
*x)*log(5))*e^(2*x) + (x^3 - 25*x^2 + (x^2 - 26*x - 25)*log(5) - 50*x)*e^x)*e^(3*e^x + 6) + 54*(2*(x^3 - 25*x^
2 + (x^2 - 25*x)*log(5))*e^(2*x) + (x^3 - 25*x^2 + (x^2 - 26*x - 25)*log(5) - 50*x)*e^x)*e^(2*e^x + 4) - 108*(
(x^3 - 25*x^2 + (x^2 - 25*x)*log(5))*e^(2*x) + (x^3 - 25*x^2 + (x^2 - 26*x - 25)*log(5) - 50*x)*e^x)*e^(e^x +
2))/(x^3 - 75*x^2 + 1875*x - 15625), x)

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maple [B]  time = 0.12, size = 113, normalized size = 3.90

method result size
risch \(\frac {81 x \left (\ln \relax (5)+x \right ) {\mathrm e}^{x}}{\left (x -25\right )^{2}}+\frac {x \left (\ln \relax (5)+x \right ) {\mathrm e}^{x +4 \,{\mathrm e}^{x}+8}}{x^{2}-50 x +625}-\frac {12 x \left (\ln \relax (5)+x \right ) {\mathrm e}^{x +3 \,{\mathrm e}^{x}+6}}{x^{2}-50 x +625}+\frac {54 x \left (\ln \relax (5)+x \right ) {\mathrm e}^{x +2 \,{\mathrm e}^{x}+4}}{x^{2}-50 x +625}-\frac {108 x \left (\ln \relax (5)+x \right ) {\mathrm e}^{{\mathrm e}^{x}+2+x}}{x^{2}-50 x +625}\) \(113\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((4*x^2-100*x)*ln(5)+4*x^3-100*x^2)*exp(x)^2+((x^2-26*x-25)*ln(5)+x^3-25*x^2-50*x)*exp(x))*exp(exp(x)+2)
^4+(((-36*x^2+900*x)*ln(5)-36*x^3+900*x^2)*exp(x)^2+((-12*x^2+312*x+300)*ln(5)-12*x^3+300*x^2+600*x)*exp(x))*e
xp(exp(x)+2)^3+(((108*x^2-2700*x)*ln(5)+108*x^3-2700*x^2)*exp(x)^2+((54*x^2-1404*x-1350)*ln(5)+54*x^3-1350*x^2
-2700*x)*exp(x))*exp(exp(x)+2)^2+(((-108*x^2+2700*x)*ln(5)-108*x^3+2700*x^2)*exp(x)^2+((-108*x^2+2808*x+2700)*
ln(5)-108*x^3+2700*x^2+5400*x)*exp(x))*exp(exp(x)+2)+((81*x^2-2106*x-2025)*ln(5)+81*x^3-2025*x^2-4050*x)*exp(x
))/(x^3-75*x^2+1875*x-15625),x,method=_RETURNVERBOSE)

[Out]

81*x*(ln(5)+x)/(x-25)^2*exp(x)+1/(x^2-50*x+625)*x*(ln(5)+x)*exp(x+4*exp(x)+8)-12/(x^2-50*x+625)*x*(ln(5)+x)*ex
p(x+3*exp(x)+6)+54/(x^2-50*x+625)*x*(ln(5)+x)*exp(x+2*exp(x)+4)-108/(x^2-50*x+625)*x*(ln(5)+x)*exp(exp(x)+2+x)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 2025 \, \int \frac {e^{x}}{x^{3} - 75 \, x^{2} + 1875 \, x - 15625}\,{d x} \log \relax (5) + \frac {2025 \, e^{25} E_{3}\left (-x + 25\right ) \log \relax (5)}{{\left (x - 25\right )}^{2}} + \frac {{\left (x^{2} e^{8} + x e^{8} \log \relax (5)\right )} e^{\left (x + 4 \, e^{x}\right )} - 12 \, {\left (x^{2} e^{6} + x e^{6} \log \relax (5)\right )} e^{\left (x + 3 \, e^{x}\right )} + 54 \, {\left (x^{2} e^{4} + x e^{4} \log \relax (5)\right )} e^{\left (x + 2 \, e^{x}\right )} - 108 \, {\left (x^{2} e^{2} + x e^{2} \log \relax (5)\right )} e^{\left (x + e^{x}\right )} + 81 \, {\left (x^{2} + x \log \relax (5)\right )} e^{x}}{x^{2} - 50 \, x + 625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4*x^2-100*x)*log(5)+4*x^3-100*x^2)*exp(x)^2+((x^2-26*x-25)*log(5)+x^3-25*x^2-50*x)*exp(x))*exp(e
xp(x)+2)^4+(((-36*x^2+900*x)*log(5)-36*x^3+900*x^2)*exp(x)^2+((-12*x^2+312*x+300)*log(5)-12*x^3+300*x^2+600*x)
*exp(x))*exp(exp(x)+2)^3+(((108*x^2-2700*x)*log(5)+108*x^3-2700*x^2)*exp(x)^2+((54*x^2-1404*x-1350)*log(5)+54*
x^3-1350*x^2-2700*x)*exp(x))*exp(exp(x)+2)^2+(((-108*x^2+2700*x)*log(5)-108*x^3+2700*x^2)*exp(x)^2+((-108*x^2+
2808*x+2700)*log(5)-108*x^3+2700*x^2+5400*x)*exp(x))*exp(exp(x)+2)+((81*x^2-2106*x-2025)*log(5)+81*x^3-2025*x^
2-4050*x)*exp(x))/(x^3-75*x^2+1875*x-15625),x, algorithm="maxima")

[Out]

2025*integrate(e^x/(x^3 - 75*x^2 + 1875*x - 15625), x)*log(5) + 2025*e^25*exp_integral_e(3, -x + 25)*log(5)/(x
 - 25)^2 + ((x^2*e^8 + x*e^8*log(5))*e^(x + 4*e^x) - 12*(x^2*e^6 + x*e^6*log(5))*e^(x + 3*e^x) + 54*(x^2*e^4 +
 x*e^4*log(5))*e^(x + 2*e^x) - 108*(x^2*e^2 + x*e^2*log(5))*e^(x + e^x) + 81*(x^2 + x*log(5))*e^x)/(x^2 - 50*x
 + 625)

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mupad [B]  time = 9.71, size = 155, normalized size = 5.34 \begin {gather*} \frac {{\mathrm {e}}^{4\,{\mathrm {e}}^x+8}\,\left (x^2\,{\mathrm {e}}^x+x\,{\mathrm {e}}^x\,\ln \relax (5)\right )}{x^2-50\,x+625}-\frac {{\mathrm {e}}^{{\mathrm {e}}^x+2}\,\left (108\,x^2\,{\mathrm {e}}^x+108\,x\,{\mathrm {e}}^x\,\ln \relax (5)\right )}{x^2-50\,x+625}-\frac {{\mathrm {e}}^{3\,{\mathrm {e}}^x+6}\,\left (12\,x^2\,{\mathrm {e}}^x+12\,x\,{\mathrm {e}}^x\,\ln \relax (5)\right )}{x^2-50\,x+625}+\frac {{\mathrm {e}}^{2\,{\mathrm {e}}^x+4}\,\left (54\,x^2\,{\mathrm {e}}^x+54\,x\,{\mathrm {e}}^x\,\ln \relax (5)\right )}{x^2-50\,x+625}+\frac {{\mathrm {e}}^x\,\left (81\,x^2+81\,\ln \relax (5)\,x\right )}{x^2-50\,x+625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x)*(4050*x + log(5)*(2106*x - 81*x^2 + 2025) + 2025*x^2 - 81*x^3) - exp(exp(x) + 2)*(exp(x)*(5400*x
+ log(5)*(2808*x - 108*x^2 + 2700) + 2700*x^2 - 108*x^3) + exp(2*x)*(log(5)*(2700*x - 108*x^2) + 2700*x^2 - 10
8*x^3)) + exp(4*exp(x) + 8)*(exp(x)*(50*x + log(5)*(26*x - x^2 + 25) + 25*x^2 - x^3) + exp(2*x)*(log(5)*(100*x
 - 4*x^2) + 100*x^2 - 4*x^3)) - exp(3*exp(x) + 6)*(exp(x)*(600*x + log(5)*(312*x - 12*x^2 + 300) + 300*x^2 - 1
2*x^3) + exp(2*x)*(log(5)*(900*x - 36*x^2) + 900*x^2 - 36*x^3)) + exp(2*exp(x) + 4)*(exp(x)*(2700*x + log(5)*(
1404*x - 54*x^2 + 1350) + 1350*x^2 - 54*x^3) + exp(2*x)*(log(5)*(2700*x - 108*x^2) + 2700*x^2 - 108*x^3)))/(18
75*x - 75*x^2 + x^3 - 15625),x)

[Out]

(exp(4*exp(x) + 8)*(x^2*exp(x) + x*exp(x)*log(5)))/(x^2 - 50*x + 625) - (exp(exp(x) + 2)*(108*x^2*exp(x) + 108
*x*exp(x)*log(5)))/(x^2 - 50*x + 625) - (exp(3*exp(x) + 6)*(12*x^2*exp(x) + 12*x*exp(x)*log(5)))/(x^2 - 50*x +
 625) + (exp(2*exp(x) + 4)*(54*x^2*exp(x) + 54*x*exp(x)*log(5)))/(x^2 - 50*x + 625) + (exp(x)*(81*x*log(5) + 8
1*x^2))/(x^2 - 50*x + 625)

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sympy [B]  time = 0.88, size = 654, normalized size = 22.55 \begin {gather*} \frac {\left (81 x^{2} + 81 x \log {\relax (5 )}\right ) e^{x}}{x^{2} - 50 x + 625} + \frac {\left (- 108 x^{8} e^{x} - 108 x^{7} e^{x} \log {\relax (5 )} + 16200 x^{7} e^{x} - 1012500 x^{6} e^{x} + 16200 x^{6} e^{x} \log {\relax (5 )} - 1012500 x^{5} e^{x} \log {\relax (5 )} + 33750000 x^{5} e^{x} - 632812500 x^{4} e^{x} + 33750000 x^{4} e^{x} \log {\relax (5 )} - 632812500 x^{3} e^{x} \log {\relax (5 )} + 6328125000 x^{3} e^{x} - 26367187500 x^{2} e^{x} + 6328125000 x^{2} e^{x} \log {\relax (5 )} - 26367187500 x e^{x} \log {\relax (5 )}\right ) e^{e^{x} + 2} + \left (- 12 x^{8} e^{x} - 12 x^{7} e^{x} \log {\relax (5 )} + 1800 x^{7} e^{x} - 112500 x^{6} e^{x} + 1800 x^{6} e^{x} \log {\relax (5 )} - 112500 x^{5} e^{x} \log {\relax (5 )} + 3750000 x^{5} e^{x} - 70312500 x^{4} e^{x} + 3750000 x^{4} e^{x} \log {\relax (5 )} - 70312500 x^{3} e^{x} \log {\relax (5 )} + 703125000 x^{3} e^{x} - 2929687500 x^{2} e^{x} + 703125000 x^{2} e^{x} \log {\relax (5 )} - 2929687500 x e^{x} \log {\relax (5 )}\right ) e^{3 e^{x} + 6} + \left (x^{8} e^{x} - 150 x^{7} e^{x} + x^{7} e^{x} \log {\relax (5 )} - 150 x^{6} e^{x} \log {\relax (5 )} + 9375 x^{6} e^{x} - 312500 x^{5} e^{x} + 9375 x^{5} e^{x} \log {\relax (5 )} - 312500 x^{4} e^{x} \log {\relax (5 )} + 5859375 x^{4} e^{x} - 58593750 x^{3} e^{x} + 5859375 x^{3} e^{x} \log {\relax (5 )} - 58593750 x^{2} e^{x} \log {\relax (5 )} + 244140625 x^{2} e^{x} + 244140625 x e^{x} \log {\relax (5 )}\right ) e^{4 e^{x} + 8} + \left (54 x^{8} e^{x} - 8100 x^{7} e^{x} + 54 x^{7} e^{x} \log {\relax (5 )} - 8100 x^{6} e^{x} \log {\relax (5 )} + 506250 x^{6} e^{x} - 16875000 x^{5} e^{x} + 506250 x^{5} e^{x} \log {\relax (5 )} - 16875000 x^{4} e^{x} \log {\relax (5 )} + 316406250 x^{4} e^{x} - 3164062500 x^{3} e^{x} + 316406250 x^{3} e^{x} \log {\relax (5 )} - 3164062500 x^{2} e^{x} \log {\relax (5 )} + 13183593750 x^{2} e^{x} + 13183593750 x e^{x} \log {\relax (5 )}\right ) e^{2 e^{x} + 4}}{x^{8} - 200 x^{7} + 17500 x^{6} - 875000 x^{5} + 27343750 x^{4} - 546875000 x^{3} + 6835937500 x^{2} - 48828125000 x + 152587890625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4*x**2-100*x)*ln(5)+4*x**3-100*x**2)*exp(x)**2+((x**2-26*x-25)*ln(5)+x**3-25*x**2-50*x)*exp(x))*
exp(exp(x)+2)**4+(((-36*x**2+900*x)*ln(5)-36*x**3+900*x**2)*exp(x)**2+((-12*x**2+312*x+300)*ln(5)-12*x**3+300*
x**2+600*x)*exp(x))*exp(exp(x)+2)**3+(((108*x**2-2700*x)*ln(5)+108*x**3-2700*x**2)*exp(x)**2+((54*x**2-1404*x-
1350)*ln(5)+54*x**3-1350*x**2-2700*x)*exp(x))*exp(exp(x)+2)**2+(((-108*x**2+2700*x)*ln(5)-108*x**3+2700*x**2)*
exp(x)**2+((-108*x**2+2808*x+2700)*ln(5)-108*x**3+2700*x**2+5400*x)*exp(x))*exp(exp(x)+2)+((81*x**2-2106*x-202
5)*ln(5)+81*x**3-2025*x**2-4050*x)*exp(x))/(x**3-75*x**2+1875*x-15625),x)

[Out]

(81*x**2 + 81*x*log(5))*exp(x)/(x**2 - 50*x + 625) + ((-108*x**8*exp(x) - 108*x**7*exp(x)*log(5) + 16200*x**7*
exp(x) - 1012500*x**6*exp(x) + 16200*x**6*exp(x)*log(5) - 1012500*x**5*exp(x)*log(5) + 33750000*x**5*exp(x) -
632812500*x**4*exp(x) + 33750000*x**4*exp(x)*log(5) - 632812500*x**3*exp(x)*log(5) + 6328125000*x**3*exp(x) -
26367187500*x**2*exp(x) + 6328125000*x**2*exp(x)*log(5) - 26367187500*x*exp(x)*log(5))*exp(exp(x) + 2) + (-12*
x**8*exp(x) - 12*x**7*exp(x)*log(5) + 1800*x**7*exp(x) - 112500*x**6*exp(x) + 1800*x**6*exp(x)*log(5) - 112500
*x**5*exp(x)*log(5) + 3750000*x**5*exp(x) - 70312500*x**4*exp(x) + 3750000*x**4*exp(x)*log(5) - 70312500*x**3*
exp(x)*log(5) + 703125000*x**3*exp(x) - 2929687500*x**2*exp(x) + 703125000*x**2*exp(x)*log(5) - 2929687500*x*e
xp(x)*log(5))*exp(3*exp(x) + 6) + (x**8*exp(x) - 150*x**7*exp(x) + x**7*exp(x)*log(5) - 150*x**6*exp(x)*log(5)
 + 9375*x**6*exp(x) - 312500*x**5*exp(x) + 9375*x**5*exp(x)*log(5) - 312500*x**4*exp(x)*log(5) + 5859375*x**4*
exp(x) - 58593750*x**3*exp(x) + 5859375*x**3*exp(x)*log(5) - 58593750*x**2*exp(x)*log(5) + 244140625*x**2*exp(
x) + 244140625*x*exp(x)*log(5))*exp(4*exp(x) + 8) + (54*x**8*exp(x) - 8100*x**7*exp(x) + 54*x**7*exp(x)*log(5)
 - 8100*x**6*exp(x)*log(5) + 506250*x**6*exp(x) - 16875000*x**5*exp(x) + 506250*x**5*exp(x)*log(5) - 16875000*
x**4*exp(x)*log(5) + 316406250*x**4*exp(x) - 3164062500*x**3*exp(x) + 316406250*x**3*exp(x)*log(5) - 316406250
0*x**2*exp(x)*log(5) + 13183593750*x**2*exp(x) + 13183593750*x*exp(x)*log(5))*exp(2*exp(x) + 4))/(x**8 - 200*x
**7 + 17500*x**6 - 875000*x**5 + 27343750*x**4 - 546875000*x**3 + 6835937500*x**2 - 48828125000*x + 1525878906
25)

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