3.13.22 \(\int \frac {e^{\frac {-30+6 x+(12-2 x) \log (5)}{5 e^x+15 x-3 x^2+(-6 x+x^2) \log (5)}} (450-180 x+18 x^2+(-360+132 x-12 x^2) \log (5)+(72-24 x+2 x^2) \log ^2(5)+e^x (180-30 x+(-70+10 x) \log (5)))}{25 e^{2 x}+225 x^2-90 x^3+9 x^4+(-180 x^2+66 x^3-6 x^4) \log (5)+(36 x^2-12 x^3+x^4) \log ^2(5)+e^x (150 x-30 x^2+(-60 x+10 x^2) \log (5))} \, dx\)

Optimal. Leaf size=32 \[ e^{\frac {2}{-x+\frac {5 e^x}{3-(6-x) (3-\log (5))}}} \]

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Rubi [F]  time = 69.38, 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 (\frac {-30+6 x+(12-2 x) \log (5)}{5 e^x+15 x-3 x^2+\left (-6 x+x^2\right ) \log (5)}\right ) \left (450-180 x+18 x^2+\left (-360+132 x-12 x^2\right ) \log (5)+\left (72-24 x+2 x^2\right ) \log ^2(5)+e^x (180-30 x+(-70+10 x) \log (5))\right )}{25 e^{2 x}+225 x^2-90 x^3+9 x^4+\left (-180 x^2+66 x^3-6 x^4\right ) \log (5)+\left (36 x^2-12 x^3+x^4\right ) \log ^2(5)+e^x \left (150 x-30 x^2+\left (-60 x+10 x^2\right ) \log (5)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-30 + 6*x + (12 - 2*x)*Log[5])/(5*E^x + 15*x - 3*x^2 + (-6*x + x^2)*Log[5]))*(450 - 180*x + 18*x^2 +
(-360 + 132*x - 12*x^2)*Log[5] + (72 - 24*x + 2*x^2)*Log[5]^2 + E^x*(180 - 30*x + (-70 + 10*x)*Log[5])))/(25*E
^(2*x) + 225*x^2 - 90*x^3 + 9*x^4 + (-180*x^2 + 66*x^3 - 6*x^4)*Log[5] + (36*x^2 - 12*x^3 + x^4)*Log[5]^2 + E^
x*(150*x - 30*x^2 + (-60*x + 10*x^2)*Log[5])),x]

[Out]

18*(5 - Log[25])^2*Defer[Int][E^((6*(-5 + x))/(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))/(5^((2*(-6 + x))/
(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))*(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5]))^2), x] - 18*(5 -
Log[25])*(8 - Log[125])*Defer[Int][(E^((6*(-5 + x))/(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))*x)/(5^((2*(
-6 + x))/(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))*(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5]))^2), x] +
4*(18 - 7*Log[5])*(3 - Log[5])*Defer[Int][(E^((6*(-5 + x))/(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))*x^2
)/(5^((2*(-6 + x))/(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))*(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])
)^2), x] - 2*(3 - Log[5])^2*Defer[Int][(E^((6*(-5 + x))/(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))*x^3)/(5
^((2*(-6 + x))/(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))*(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5]))^2)
, x] + 2*(18 - 7*Log[5])*Defer[Int][E^((6*(-5 + x))/(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))/(5^((2*(-6
+ x))/(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))*(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5]))), x] - 2*(3
- Log[5])*Defer[Int][(E^((6*(-5 + x))/(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))*x)/(5^((2*(-6 + x))/(5*E
^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))*(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5]))), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2\ 5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) \left (5 e^x (18+x (-3+\log (5))-7 \log (5))+(15+x (-3+\log (5))-6 \log (5))^2\right )}{\left (5 e^x+x (15+x (-3+\log (5))-6 \log (5))\right )^2} \, dx\\ &=2 \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) \left (5 e^x (18+x (-3+\log (5))-7 \log (5))+(15+x (-3+\log (5))-6 \log (5))^2\right )}{\left (5 e^x+x (15+x (-3+\log (5))-6 \log (5))\right )^2} \, dx\\ &=2 \int \left (\frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) (18-x (3-\log (5))-7 \log (5))}{5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )}+\frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) \left (2 x^2 (18-7 \log (5)) (3-\log (5))-x^3 (3-\log (5))^2-9 x \left (40-31 \log (5)+6 \log ^2(5)\right )+9 (5-\log (25))^2\right )}{\left (5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )\right )^2}\right ) \, dx\\ &=2 \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) (18-x (3-\log (5))-7 \log (5))}{5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )} \, dx+2 \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) \left (2 x^2 (18-7 \log (5)) (3-\log (5))-x^3 (3-\log (5))^2-9 x \left (40-31 \log (5)+6 \log ^2(5)\right )+9 (5-\log (25))^2\right )}{\left (5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )\right )^2} \, dx\\ &=2 \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) (18+x (-3+\log (5))-7 \log (5))}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))} \, dx+2 \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) \left (2 x^2 (18-7 \log (5)) (3-\log (5))-x^3 (3-\log (5))^2-9 x \left (40-31 \log (5)+6 \log ^2(5)\right )+9 (5-\log (25))^2\right )}{\left (5 e^x+x (15+x (-3+\log (5))-6 \log (5))\right )^2} \, dx\\ &=2 \int \left (\frac {18\ 5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) \left (1-\frac {7 \log (5)}{18}\right )}{5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )}+\frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x (-3+\log (5))}{5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )}\right ) \, dx+2 \int \left (\frac {2\ 5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x^2 (18-7 \log (5)) (3-\log (5))}{\left (5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )\right )^2}-\frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x^3 (3-\log (5))^2}{\left (5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )\right )^2}+\frac {9\ 5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) (5-\log (25))^2}{\left (5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )\right )^2}+\frac {9\ 5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x (5-\log (25)) (-8+\log (125))}{\left (5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )\right )^2}\right ) \, dx\\ &=(2 (18-7 \log (5))) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right )}{5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )} \, dx+(4 (18-7 \log (5)) (3-\log (5))) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x^2}{\left (5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )\right )^2} \, dx-\left (2 (3-\log (5))^2\right ) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x^3}{\left (5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )\right )^2} \, dx+(2 (-3+\log (5))) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x}{5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )} \, dx+\left (18 (5-\log (25))^2\right ) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right )}{\left (5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )\right )^2} \, dx-(18 (5-\log (25)) (8-\log (125))) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x}{\left (5 e^x+15 x \left (1-\frac {2 \log (5)}{5}\right )-3 x^2 \left (1-\frac {\log (5)}{3}\right )\right )^2} \, dx\\ &=(2 (18-7 \log (5))) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right )}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))} \, dx+(4 (18-7 \log (5)) (3-\log (5))) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x^2}{\left (5 e^x+x (15+x (-3+\log (5))-6 \log (5))\right )^2} \, dx-\left (2 (3-\log (5))^2\right ) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x^3}{\left (5 e^x+x (15+x (-3+\log (5))-6 \log (5))\right )^2} \, dx+(2 (-3+\log (5))) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))} \, dx+\left (18 (5-\log (25))^2\right ) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right )}{\left (5 e^x+x (15+x (-3+\log (5))-6 \log (5))\right )^2} \, dx-(18 (5-\log (25)) (8-\log (125))) \int \frac {5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \exp \left (\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}\right ) x}{\left (5 e^x+x (15+x (-3+\log (5))-6 \log (5))\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.32, size = 59, normalized size = 1.84 \begin {gather*} 5^{-\frac {2 (-6+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} e^{\frac {6 (-5+x)}{5 e^x+x (15+x (-3+\log (5))-6 \log (5))}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((-30 + 6*x + (12 - 2*x)*Log[5])/(5*E^x + 15*x - 3*x^2 + (-6*x + x^2)*Log[5]))*(450 - 180*x + 18*
x^2 + (-360 + 132*x - 12*x^2)*Log[5] + (72 - 24*x + 2*x^2)*Log[5]^2 + E^x*(180 - 30*x + (-70 + 10*x)*Log[5])))
/(25*E^(2*x) + 225*x^2 - 90*x^3 + 9*x^4 + (-180*x^2 + 66*x^3 - 6*x^4)*Log[5] + (36*x^2 - 12*x^3 + x^4)*Log[5]^
2 + E^x*(150*x - 30*x^2 + (-60*x + 10*x^2)*Log[5])),x]

[Out]

E^((6*(-5 + x))/(5*E^x + x*(15 + x*(-3 + Log[5]) - 6*Log[5])))/5^((2*(-6 + x))/(5*E^x + x*(15 + x*(-3 + Log[5]
) - 6*Log[5])))

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fricas [A]  time = 0.63, size = 40, normalized size = 1.25 \begin {gather*} e^{\left (\frac {2 \, {\left ({\left (x - 6\right )} \log \relax (5) - 3 \, x + 15\right )}}{3 \, x^{2} - {\left (x^{2} - 6 \, x\right )} \log \relax (5) - 15 \, x - 5 \, e^{x}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x-70)*log(5)-30*x+180)*exp(x)+(2*x^2-24*x+72)*log(5)^2+(-12*x^2+132*x-360)*log(5)+18*x^2-180*x
+450)*exp(((-2*x+12)*log(5)+6*x-30)/(5*exp(x)+(x^2-6*x)*log(5)-3*x^2+15*x))/(25*exp(x)^2+((10*x^2-60*x)*log(5)
-30*x^2+150*x)*exp(x)+(x^4-12*x^3+36*x^2)*log(5)^2+(-6*x^4+66*x^3-180*x^2)*log(5)+9*x^4-90*x^3+225*x^2),x, alg
orithm="fricas")

[Out]

e^(2*((x - 6)*log(5) - 3*x + 15)/(3*x^2 - (x^2 - 6*x)*log(5) - 15*x - 5*e^x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left ({\left (x^{2} - 12 \, x + 36\right )} \log \relax (5)^{2} + 9 \, x^{2} + 5 \, {\left ({\left (x - 7\right )} \log \relax (5) - 3 \, x + 18\right )} e^{x} - 6 \, {\left (x^{2} - 11 \, x + 30\right )} \log \relax (5) - 90 \, x + 225\right )} e^{\left (\frac {2 \, {\left ({\left (x - 6\right )} \log \relax (5) - 3 \, x + 15\right )}}{3 \, x^{2} - {\left (x^{2} - 6 \, x\right )} \log \relax (5) - 15 \, x - 5 \, e^{x}}\right )}}{9 \, x^{4} - 90 \, x^{3} + {\left (x^{4} - 12 \, x^{3} + 36 \, x^{2}\right )} \log \relax (5)^{2} + 225 \, x^{2} - 10 \, {\left (3 \, x^{2} - {\left (x^{2} - 6 \, x\right )} \log \relax (5) - 15 \, x\right )} e^{x} - 6 \, {\left (x^{4} - 11 \, x^{3} + 30 \, x^{2}\right )} \log \relax (5) + 25 \, e^{\left (2 \, x\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x-70)*log(5)-30*x+180)*exp(x)+(2*x^2-24*x+72)*log(5)^2+(-12*x^2+132*x-360)*log(5)+18*x^2-180*x
+450)*exp(((-2*x+12)*log(5)+6*x-30)/(5*exp(x)+(x^2-6*x)*log(5)-3*x^2+15*x))/(25*exp(x)^2+((10*x^2-60*x)*log(5)
-30*x^2+150*x)*exp(x)+(x^4-12*x^3+36*x^2)*log(5)^2+(-6*x^4+66*x^3-180*x^2)*log(5)+9*x^4-90*x^3+225*x^2),x, alg
orithm="giac")

[Out]

integrate(2*((x^2 - 12*x + 36)*log(5)^2 + 9*x^2 + 5*((x - 7)*log(5) - 3*x + 18)*e^x - 6*(x^2 - 11*x + 30)*log(
5) - 90*x + 225)*e^(2*((x - 6)*log(5) - 3*x + 15)/(3*x^2 - (x^2 - 6*x)*log(5) - 15*x - 5*e^x))/(9*x^4 - 90*x^3
+ (x^4 - 12*x^3 + 36*x^2)*log(5)^2 + 225*x^2 - 10*(3*x^2 - (x^2 - 6*x)*log(5) - 15*x)*e^x - 6*(x^4 - 11*x^3 +
30*x^2)*log(5) + 25*e^(2*x)), x)

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maple [A]  time = 0.71, size = 43, normalized size = 1.34

method	result	size
risch	\({\mathrm e}^{-\frac {2 \left (x \ln \relax (5)-6 \ln \relax (5)-3 x +15\right )}{x^{2} \ln \relax (5)-6 x \ln \relax (5)-3 x^{2}+5 \,{\mathrm e}^{x}+15 x}}\)	\(43\)
norman	\(\frac {\left (-6 \ln \relax (5)+15\right ) x \,{\mathrm e}^{\frac {\left (-2 x +12\right ) \ln \relax (5)+6 x -30}{5 \,{\mathrm e}^{x}+\left (x^{2}-6 x \right ) \ln \relax (5)-3 x^{2}+15 x}}+\left (\ln \relax (5)-3\right ) x^{2} {\mathrm e}^{\frac {\left (-2 x +12\right ) \ln \relax (5)+6 x -30}{5 \,{\mathrm e}^{x}+\left (x^{2}-6 x \right ) \ln \relax (5)-3 x^{2}+15 x}}+5 \,{\mathrm e}^{x} {\mathrm e}^{\frac {\left (-2 x +12\right ) \ln \relax (5)+6 x -30}{5 \,{\mathrm e}^{x}+\left (x^{2}-6 x \right ) \ln \relax (5)-3 x^{2}+15 x}}}{x^{2} \ln \relax (5)-6 x \ln \relax (5)-3 x^{2}+5 \,{\mathrm e}^{x}+15 x}\)	\(169\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((10*x-70)*ln(5)-30*x+180)*exp(x)+(2*x^2-24*x+72)*ln(5)^2+(-12*x^2+132*x-360)*ln(5)+18*x^2-180*x+450)*exp
(((-2*x+12)*ln(5)+6*x-30)/(5*exp(x)+(x^2-6*x)*ln(5)-3*x^2+15*x))/(25*exp(x)^2+((10*x^2-60*x)*ln(5)-30*x^2+150*
x)*exp(x)+(x^4-12*x^3+36*x^2)*ln(5)^2+(-6*x^4+66*x^3-180*x^2)*ln(5)+9*x^4-90*x^3+225*x^2),x,method=_RETURNVERB
OSE)

[Out]

exp(-2*(x*ln(5)-6*ln(5)-3*x+15)/(x^2*ln(5)-6*x*ln(5)-3*x^2+5*exp(x)+15*x))

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maxima [B]  time = 0.84, size = 112, normalized size = 3.50 \begin {gather*} e^{\left (-\frac {2 \, x \log \relax (5)}{x^{2} {\left (\log \relax (5) - 3\right )} - 3 \, x {\left (2 \, \log \relax (5) - 5\right )} + 5 \, e^{x}} + \frac {6 \, x}{x^{2} {\left (\log \relax (5) - 3\right )} - 3 \, x {\left (2 \, \log \relax (5) - 5\right )} + 5 \, e^{x}} + \frac {12 \, \log \relax (5)}{x^{2} {\left (\log \relax (5) - 3\right )} - 3 \, x {\left (2 \, \log \relax (5) - 5\right )} + 5 \, e^{x}} - \frac {30}{x^{2} {\left (\log \relax (5) - 3\right )} - 3 \, x {\left (2 \, \log \relax (5) - 5\right )} + 5 \, e^{x}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x-70)*log(5)-30*x+180)*exp(x)+(2*x^2-24*x+72)*log(5)^2+(-12*x^2+132*x-360)*log(5)+18*x^2-180*x
+450)*exp(((-2*x+12)*log(5)+6*x-30)/(5*exp(x)+(x^2-6*x)*log(5)-3*x^2+15*x))/(25*exp(x)^2+((10*x^2-60*x)*log(5)
-30*x^2+150*x)*exp(x)+(x^4-12*x^3+36*x^2)*log(5)^2+(-6*x^4+66*x^3-180*x^2)*log(5)+9*x^4-90*x^3+225*x^2),x, alg
orithm="maxima")

[Out]

e^(-2*x*log(5)/(x^2*(log(5) - 3) - 3*x*(2*log(5) - 5) + 5*e^x) + 6*x/(x^2*(log(5) - 3) - 3*x*(2*log(5) - 5) +
5*e^x) + 12*log(5)/(x^2*(log(5) - 3) - 3*x*(2*log(5) - 5) + 5*e^x) - 30/(x^2*(log(5) - 3) - 3*x*(2*log(5) - 5)
+ 5*e^x))

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mupad [B]  time = 1.82, size = 92, normalized size = 2.88 \begin {gather*} {\left (\frac {1}{25}\right )}^{\frac {x-6}{15\,x+5\,{\mathrm {e}}^x-6\,x\,\ln \relax (5)+x^2\,\ln \relax (5)-3\,x^2}}\,{\mathrm {e}}^{\frac {6\,x}{15\,x+5\,{\mathrm {e}}^x-6\,x\,\ln \relax (5)+x^2\,\ln \relax (5)-3\,x^2}}\,{\mathrm {e}}^{-\frac {30}{15\,x+5\,{\mathrm {e}}^x-6\,x\,\ln \relax (5)+x^2\,\ln \relax (5)-3\,x^2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(log(5)*(2*x - 12) - 6*x + 30)/(15*x + 5*exp(x) - log(5)*(6*x - x^2) - 3*x^2))*(exp(x)*(log(5)*(10*x
- 70) - 30*x + 180) - log(5)*(12*x^2 - 132*x + 360) - 180*x + log(5)^2*(2*x^2 - 24*x + 72) + 18*x^2 + 450))/(
25*exp(2*x) - log(5)*(180*x^2 - 66*x^3 + 6*x^4) + log(5)^2*(36*x^2 - 12*x^3 + x^4) + 225*x^2 - 90*x^3 + 9*x^4
- exp(x)*(log(5)*(60*x - 10*x^2) - 150*x + 30*x^2)),x)

[Out]

(1/25)^((x - 6)/(15*x + 5*exp(x) - 6*x*log(5) + x^2*log(5) - 3*x^2))*exp((6*x)/(15*x + 5*exp(x) - 6*x*log(5) +
x^2*log(5) - 3*x^2))*exp(-30/(15*x + 5*exp(x) - 6*x*log(5) + x^2*log(5) - 3*x^2))

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sympy [A]  time = 1.34, size = 37, normalized size = 1.16 \begin {gather*} e^{\frac {6 x + \left (12 - 2 x\right ) \log {\relax (5 )} - 30}{- 3 x^{2} + 15 x + \left (x^{2} - 6 x\right ) \log {\relax (5 )} + 5 e^{x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((10*x-70)*ln(5)-30*x+180)*exp(x)+(2*x**2-24*x+72)*ln(5)**2+(-12*x**2+132*x-360)*ln(5)+18*x**2-180*
x+450)*exp(((-2*x+12)*ln(5)+6*x-30)/(5*exp(x)+(x**2-6*x)*ln(5)-3*x**2+15*x))/(25*exp(x)**2+((10*x**2-60*x)*ln(
5)-30*x**2+150*x)*exp(x)+(x**4-12*x**3+36*x**2)*ln(5)**2+(-6*x**4+66*x**3-180*x**2)*ln(5)+9*x**4-90*x**3+225*x
**2),x)

[Out]

exp((6*x + (12 - 2*x)*log(5) - 30)/(-3*x**2 + 15*x + (x**2 - 6*x)*log(5) + 5*exp(x)))

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