3.81.68 \(\int \frac {e^x (10 x^3-10 x^4+e^3 (-10 x^2+10 x^3))+e^x (20 e^3 x^2-20 x^3) \log (e^3-x)+e^x (10 e^3 x-10 x^2) \log ^2(e^3-x)+\log (-9+5 e^x) (-54 x^3+e^3 (-36 x+54 x^2)+e^x (30 x^3+e^3 (20 x-30 x^2))+(-36 x+72 e^3 x-72 x^2+e^x (20 x-40 e^3 x+40 x^2)) \log (e^3-x)+(18 e^3-18 x+e^x (-10 e^3+10 x)) \log ^2(e^3-x))}{9 x^5-18 x^6+9 x^7+e^3 (-9 x^4+18 x^5-9 x^6)+e^x (-5 x^5+10 x^6-5 x^7+e^3 (5 x^4-10 x^5+5 x^6))+(-36 x^5+36 x^6+e^3 (36 x^4-36 x^5)+e^x (20 x^5-20 x^6+e^3 (-20 x^4+20 x^5))) \log (e^3-x)+(-18 x^4+54 x^5+e^3 (18 x^3-54 x^4)+e^x (10 x^4-30 x^5+e^3 (-10 x^3+30 x^4))) \log ^2(e^3-x)+(-36 e^3 x^3+36 x^4+e^x (20 e^3 x^3-20 x^4)) \log ^3(e^3-x)+(-9 e^3 x^2+9 x^3+e^x (5 e^3 x^2-5 x^3)) \log ^4(e^3-x)} \, dx\)

Optimal. Leaf size=33 \[ \frac {2 \log \left (1+5 \left (-2+e^x\right )\right )}{x \left (-x+\left (x+\log \left (e^3-x\right )\right )^2\right )} \]

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Rubi [F]  time = 24.51, 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 (10 x^3-10 x^4+e^3 \left (-10 x^2+10 x^3\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (-9+5 e^x\right ) \left (-54 x^3+e^3 \left (-36 x+54 x^2\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-36 x+72 e^3 x-72 x^2+e^x \left (20 x-40 e^3 x+40 x^2\right )\right ) \log \left (e^3-x\right )+\left (18 e^3-18 x+e^x \left (-10 e^3+10 x\right )\right ) \log ^2\left (e^3-x\right )\right )}{9 x^5-18 x^6+9 x^7+e^3 \left (-9 x^4+18 x^5-9 x^6\right )+e^x \left (-5 x^5+10 x^6-5 x^7+e^3 \left (5 x^4-10 x^5+5 x^6\right )\right )+\left (-36 x^5+36 x^6+e^3 \left (36 x^4-36 x^5\right )+e^x \left (20 x^5-20 x^6+e^3 \left (-20 x^4+20 x^5\right )\right )\right ) \log \left (e^3-x\right )+\left (-18 x^4+54 x^5+e^3 \left (18 x^3-54 x^4\right )+e^x \left (10 x^4-30 x^5+e^3 \left (-10 x^3+30 x^4\right )\right )\right ) \log ^2\left (e^3-x\right )+\left (-36 e^3 x^3+36 x^4+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (-9 e^3 x^2+9 x^3+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^x*(10*x^3 - 10*x^4 + E^3*(-10*x^2 + 10*x^3)) + E^x*(20*E^3*x^2 - 20*x^3)*Log[E^3 - x] + E^x*(10*E^3*x -
10*x^2)*Log[E^3 - x]^2 + Log[-9 + 5*E^x]*(-54*x^3 + E^3*(-36*x + 54*x^2) + E^x*(30*x^3 + E^3*(20*x - 30*x^2))
+ (-36*x + 72*E^3*x - 72*x^2 + E^x*(20*x - 40*E^3*x + 40*x^2))*Log[E^3 - x] + (18*E^3 - 18*x + E^x*(-10*E^3 +
10*x))*Log[E^3 - x]^2))/(9*x^5 - 18*x^6 + 9*x^7 + E^3*(-9*x^4 + 18*x^5 - 9*x^6) + E^x*(-5*x^5 + 10*x^6 - 5*x^
7 + E^3*(5*x^4 - 10*x^5 + 5*x^6)) + (-36*x^5 + 36*x^6 + E^3*(36*x^4 - 36*x^5) + E^x*(20*x^5 - 20*x^6 + E^3*(-2
0*x^4 + 20*x^5)))*Log[E^3 - x] + (-18*x^4 + 54*x^5 + E^3*(18*x^3 - 54*x^4) + E^x*(10*x^4 - 30*x^5 + E^3*(-10*x
^3 + 30*x^4)))*Log[E^3 - x]^2 + (-36*E^3*x^3 + 36*x^4 + E^x*(20*E^3*x^3 - 20*x^4))*Log[E^3 - x]^3 + (-9*E^3*x^
2 + 9*x^3 + E^x*(5*E^3*x^2 - 5*x^3))*Log[E^3 - x]^4),x]

[Out]

-4*Defer[Int][Log[-9 + 5*E^x]/(-x + x^2 + 2*x*Log[E^3 - x] + Log[E^3 - x]^2)^2, x] + 2*Defer[Int][Log[-9 + 5*E
^x]/((E^3 - x)*(-x + x^2 + 2*x*Log[E^3 - x] + Log[E^3 - x]^2)^2), x] + 4*E^3*Defer[Int][Log[-9 + 5*E^x]/((E^3
- x)*(-x + x^2 + 2*x*Log[E^3 - x] + Log[E^3 - x]^2)^2), x] + 2*(1 - 2*E^3)*Defer[Int][Log[-9 + 5*E^x]/((E^3 -
x)*(-x + x^2 + 2*x*Log[E^3 - x] + Log[E^3 - x]^2)^2), x] + 2*Defer[Int][Log[-9 + 5*E^x]/(x*(-x + x^2 + 2*x*Log
[E^3 - x] + Log[E^3 - x]^2)^2), x] + 4*Defer[Int][(Log[-9 + 5*E^x]*Log[E^3 - x])/((E^3 - x)*(-x + x^2 + 2*x*Lo
g[E^3 - x] + Log[E^3 - x]^2)^2), x] - 4*(1 - E^(-3))*Defer[Int][(Log[-9 + 5*E^x]*Log[E^3 - x])/((E^3 - x)*(-x
+ x^2 + 2*x*Log[E^3 - x] + Log[E^3 - x]^2)^2), x] - 4*(1 - E^(-3))*Defer[Int][(Log[-9 + 5*E^x]*Log[E^3 - x])/(
x*(-x + x^2 + 2*x*Log[E^3 - x] + Log[E^3 - x]^2)^2), x] + 2*Defer[Int][1/(x*(-x + x^2 + 2*x*Log[E^3 - x] + Log
[E^3 - x]^2)), x] + 18*Defer[Int][1/((-9 + 5*E^x)*x*(-x + x^2 + 2*x*Log[E^3 - x] + Log[E^3 - x]^2)), x] - 2*De
fer[Int][Log[-9 + 5*E^x]/(x^2*(-x + x^2 + 2*x*Log[E^3 - x] + Log[E^3 - x]^2)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (\frac {5 e^x x \left ((-1+x) x+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )}{-9+5 e^x}-\frac {\log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 x (-2+3 x)-2 x \left (1-2 e^3+2 x\right ) \log \left (e^3-x\right )+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )}{e^3-x}\right )}{x^2 \left ((-1+x) x+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2} \, dx\\ &=2 \int \frac {\frac {5 e^x x \left ((-1+x) x+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )}{-9+5 e^x}-\frac {\log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 x (-2+3 x)-2 x \left (1-2 e^3+2 x\right ) \log \left (e^3-x\right )+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )}{e^3-x}}{x^2 \left ((-1+x) x+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2} \, dx\\ &=2 \int \left (\frac {9}{\left (-9+5 e^x\right ) x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )}+\frac {-e^3 x^2+\left (1+e^3\right ) x^3-x^4+2 e^3 x \log \left (-9+5 e^x\right )-3 e^3 x^2 \log \left (-9+5 e^x\right )+3 x^3 \log \left (-9+5 e^x\right )+2 e^3 x^2 \log \left (e^3-x\right )-2 x^3 \log \left (e^3-x\right )+2 \left (1-2 e^3\right ) x \log \left (-9+5 e^x\right ) \log \left (e^3-x\right )+4 x^2 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right )+e^3 x \log ^2\left (e^3-x\right )-x^2 \log ^2\left (e^3-x\right )-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )+x \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (x-x^2-2 x \log \left (e^3-x\right )-\log ^2\left (e^3-x\right )\right )^2}\right ) \, dx\\ &=2 \int \frac {-e^3 x^2+\left (1+e^3\right ) x^3-x^4+2 e^3 x \log \left (-9+5 e^x\right )-3 e^3 x^2 \log \left (-9+5 e^x\right )+3 x^3 \log \left (-9+5 e^x\right )+2 e^3 x^2 \log \left (e^3-x\right )-2 x^3 \log \left (e^3-x\right )+2 \left (1-2 e^3\right ) x \log \left (-9+5 e^x\right ) \log \left (e^3-x\right )+4 x^2 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right )+e^3 x \log ^2\left (e^3-x\right )-x^2 \log ^2\left (e^3-x\right )-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )+x \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (x-x^2-2 x \log \left (e^3-x\right )-\log ^2\left (e^3-x\right )\right )^2} \, dx+18 \int \frac {1}{\left (-9+5 e^x\right ) x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx\\ &=2 \int \frac {x \left ((-1+x) x+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )+\frac {\log \left (-9+5 e^x\right ) \left (e^3 (2-3 x) x+3 x^3+2 x \left (1-2 e^3+2 x\right ) \log \left (e^3-x\right )+\left (-e^3+x\right ) \log ^2\left (e^3-x\right )\right )}{e^3-x}}{x^2 \left ((-1+x) x+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2} \, dx+18 \int \frac {1}{\left (-9+5 e^x\right ) x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx\\ &=2 \int \left (\frac {\log \left (-9+5 e^x\right ) \left (e^3+\left (1-2 e^3\right ) x+2 x^2+2 \left (1-e^3\right ) \log \left (e^3-x\right )+2 x \log \left (e^3-x\right )\right )}{\left (e^3-x\right ) x \left (x-x^2-2 x \log \left (e^3-x\right )-\log ^2\left (e^3-x\right )\right )^2}+\frac {x-\log \left (-9+5 e^x\right )}{x^2 \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )}\right ) \, dx+18 \int \frac {1}{\left (-9+5 e^x\right ) x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx\\ &=2 \int \frac {\log \left (-9+5 e^x\right ) \left (e^3+\left (1-2 e^3\right ) x+2 x^2+2 \left (1-e^3\right ) \log \left (e^3-x\right )+2 x \log \left (e^3-x\right )\right )}{\left (e^3-x\right ) x \left (x-x^2-2 x \log \left (e^3-x\right )-\log ^2\left (e^3-x\right )\right )^2} \, dx+2 \int \frac {x-\log \left (-9+5 e^x\right )}{x^2 \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx+18 \int \frac {1}{\left (-9+5 e^x\right ) x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx\\ &=2 \int \left (\frac {\log \left (-9+5 e^x\right ) \left (e^3+\left (1-2 e^3\right ) x+2 x^2+2 \left (1-e^3\right ) \log \left (e^3-x\right )+2 x \log \left (e^3-x\right )\right )}{e^3 \left (e^3-x\right ) \left (x-x^2-2 x \log \left (e^3-x\right )-\log ^2\left (e^3-x\right )\right )^2}+\frac {\log \left (-9+5 e^x\right ) \left (e^3+\left (1-2 e^3\right ) x+2 x^2+2 \left (1-e^3\right ) \log \left (e^3-x\right )+2 x \log \left (e^3-x\right )\right )}{e^3 x \left (x-x^2-2 x \log \left (e^3-x\right )-\log ^2\left (e^3-x\right )\right )^2}\right ) \, dx+2 \int \left (\frac {1}{x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )}-\frac {\log \left (-9+5 e^x\right )}{x^2 \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )}\right ) \, dx+18 \int \frac {1}{\left (-9+5 e^x\right ) x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx\\ &=2 \int \frac {1}{x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx-2 \int \frac {\log \left (-9+5 e^x\right )}{x^2 \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx+18 \int \frac {1}{\left (-9+5 e^x\right ) x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx+\frac {2 \int \frac {\log \left (-9+5 e^x\right ) \left (e^3+\left (1-2 e^3\right ) x+2 x^2+2 \left (1-e^3\right ) \log \left (e^3-x\right )+2 x \log \left (e^3-x\right )\right )}{\left (e^3-x\right ) \left (x-x^2-2 x \log \left (e^3-x\right )-\log ^2\left (e^3-x\right )\right )^2} \, dx}{e^3}+\frac {2 \int \frac {\log \left (-9+5 e^x\right ) \left (e^3+\left (1-2 e^3\right ) x+2 x^2+2 \left (1-e^3\right ) \log \left (e^3-x\right )+2 x \log \left (e^3-x\right )\right )}{x \left (x-x^2-2 x \log \left (e^3-x\right )-\log ^2\left (e^3-x\right )\right )^2} \, dx}{e^3}\\ &=2 \int \frac {1}{x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx-2 \int \frac {\log \left (-9+5 e^x\right )}{x^2 \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx+18 \int \frac {1}{\left (-9+5 e^x\right ) x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \, dx+\frac {2 \int \left (-\frac {\left (-1+2 e^3\right ) \log \left (-9+5 e^x\right )}{\left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2}+\frac {e^3 \log \left (-9+5 e^x\right )}{x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2}+\frac {2 x \log \left (-9+5 e^x\right )}{\left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2}+\frac {2 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right )}{\left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2}-\frac {2 \left (-1+e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right )}{x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2}\right ) \, dx}{e^3}+\frac {2 \int \left (\frac {e^3 \log \left (-9+5 e^x\right )}{\left (e^3-x\right ) \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2}-\frac {\left (-1+2 e^3\right ) x \log \left (-9+5 e^x\right )}{\left (e^3-x\right ) \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2}+\frac {2 x^2 \log \left (-9+5 e^x\right )}{\left (e^3-x\right ) \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2}-\frac {2 \left (-1+e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right )}{\left (e^3-x\right ) \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2}+\frac {2 x \log \left (-9+5 e^x\right ) \log \left (e^3-x\right )}{\left (e^3-x\right ) \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )^2}\right ) \, dx}{e^3}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.24, size = 43, normalized size = 1.30 \begin {gather*} \frac {2 \log \left (-9+5 e^x\right )}{x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^x*(10*x^3 - 10*x^4 + E^3*(-10*x^2 + 10*x^3)) + E^x*(20*E^3*x^2 - 20*x^3)*Log[E^3 - x] + E^x*(10*E
^3*x - 10*x^2)*Log[E^3 - x]^2 + Log[-9 + 5*E^x]*(-54*x^3 + E^3*(-36*x + 54*x^2) + E^x*(30*x^3 + E^3*(20*x - 30
*x^2)) + (-36*x + 72*E^3*x - 72*x^2 + E^x*(20*x - 40*E^3*x + 40*x^2))*Log[E^3 - x] + (18*E^3 - 18*x + E^x*(-10
*E^3 + 10*x))*Log[E^3 - x]^2))/(9*x^5 - 18*x^6 + 9*x^7 + E^3*(-9*x^4 + 18*x^5 - 9*x^6) + E^x*(-5*x^5 + 10*x^6
- 5*x^7 + E^3*(5*x^4 - 10*x^5 + 5*x^6)) + (-36*x^5 + 36*x^6 + E^3*(36*x^4 - 36*x^5) + E^x*(20*x^5 - 20*x^6 + E
^3*(-20*x^4 + 20*x^5)))*Log[E^3 - x] + (-18*x^4 + 54*x^5 + E^3*(18*x^3 - 54*x^4) + E^x*(10*x^4 - 30*x^5 + E^3*
(-10*x^3 + 30*x^4)))*Log[E^3 - x]^2 + (-36*E^3*x^3 + 36*x^4 + E^x*(20*E^3*x^3 - 20*x^4))*Log[E^3 - x]^3 + (-9*
E^3*x^2 + 9*x^3 + E^x*(5*E^3*x^2 - 5*x^3))*Log[E^3 - x]^4),x]

[Out]

(2*Log[-9 + 5*E^x])/(x*(-x + x^2 + 2*x*Log[E^3 - x] + Log[E^3 - x]^2))

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fricas [A]  time = 0.66, size = 43, normalized size = 1.30 \begin {gather*} \frac {2 \, \log \left (5 \, e^{x} - 9\right )}{x^{3} + 2 \, x^{2} \log \left (-x + e^{3}\right ) + x \log \left (-x + e^{3}\right )^{2} - x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*log(-x+exp(3))^2+((-40*x*exp(3)+40*x^2+20*x)*exp(x)+72*x
*exp(3)-72*x^2-36*x)*log(-x+exp(3))+((-30*x^2+20*x)*exp(3)+30*x^3)*exp(x)+(54*x^2-36*x)*exp(3)-54*x^3)*log(5*e
xp(x)-9)+(10*x*exp(3)-10*x^2)*exp(x)*log(-x+exp(3))^2+(20*x^2*exp(3)-20*x^3)*exp(x)*log(-x+exp(3))+((10*x^3-10
*x^2)*exp(3)-10*x^4+10*x^3)*exp(x))/(((5*x^2*exp(3)-5*x^3)*exp(x)-9*x^2*exp(3)+9*x^3)*log(-x+exp(3))^4+((20*x^
3*exp(3)-20*x^4)*exp(x)-36*x^3*exp(3)+36*x^4)*log(-x+exp(3))^3+(((30*x^4-10*x^3)*exp(3)-30*x^5+10*x^4)*exp(x)+
(-54*x^4+18*x^3)*exp(3)+54*x^5-18*x^4)*log(-x+exp(3))^2+(((20*x^5-20*x^4)*exp(3)-20*x^6+20*x^5)*exp(x)+(-36*x^
5+36*x^4)*exp(3)+36*x^6-36*x^5)*log(-x+exp(3))+((5*x^6-10*x^5+5*x^4)*exp(3)-5*x^7+10*x^6-5*x^5)*exp(x)+(-9*x^6
+18*x^5-9*x^4)*exp(3)+9*x^7-18*x^6+9*x^5),x, algorithm="fricas")

[Out]

2*log(5*e^x - 9)/(x^3 + 2*x^2*log(-x + e^3) + x*log(-x + e^3)^2 - x^2)

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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(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*log(-x+exp(3))^2+((-40*x*exp(3)+40*x^2+20*x)*exp(x)+72*x
*exp(3)-72*x^2-36*x)*log(-x+exp(3))+((-30*x^2+20*x)*exp(3)+30*x^3)*exp(x)+(54*x^2-36*x)*exp(3)-54*x^3)*log(5*e
xp(x)-9)+(10*x*exp(3)-10*x^2)*exp(x)*log(-x+exp(3))^2+(20*x^2*exp(3)-20*x^3)*exp(x)*log(-x+exp(3))+((10*x^3-10
*x^2)*exp(3)-10*x^4+10*x^3)*exp(x))/(((5*x^2*exp(3)-5*x^3)*exp(x)-9*x^2*exp(3)+9*x^3)*log(-x+exp(3))^4+((20*x^
3*exp(3)-20*x^4)*exp(x)-36*x^3*exp(3)+36*x^4)*log(-x+exp(3))^3+(((30*x^4-10*x^3)*exp(3)-30*x^5+10*x^4)*exp(x)+
(-54*x^4+18*x^3)*exp(3)+54*x^5-18*x^4)*log(-x+exp(3))^2+(((20*x^5-20*x^4)*exp(3)-20*x^6+20*x^5)*exp(x)+(-36*x^
5+36*x^4)*exp(3)+36*x^6-36*x^5)*log(-x+exp(3))+((5*x^6-10*x^5+5*x^4)*exp(3)-5*x^7+10*x^6-5*x^5)*exp(x)+(-9*x^6
+18*x^5-9*x^4)*exp(3)+9*x^7-18*x^6+9*x^5),x, algorithm="giac")

[Out]

Timed out

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maple [A]  time = 0.08, size = 41, normalized size = 1.24

method	result	size
risch	\(\frac {2 \ln \left (5 \,{\mathrm e}^{x}-9\right )}{x \left (x^{2}+2 x \ln \left (-x +{\mathrm e}^{3}\right )+\ln \left (-x +{\mathrm e}^{3}\right )^{2}-x \right )}\)	\(41\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*ln(-x+exp(3))^2+((-40*x*exp(3)+40*x^2+20*x)*exp(x)+72*x*exp(3)
-72*x^2-36*x)*ln(-x+exp(3))+((-30*x^2+20*x)*exp(3)+30*x^3)*exp(x)+(54*x^2-36*x)*exp(3)-54*x^3)*ln(5*exp(x)-9)+
(10*x*exp(3)-10*x^2)*exp(x)*ln(-x+exp(3))^2+(20*x^2*exp(3)-20*x^3)*exp(x)*ln(-x+exp(3))+((10*x^3-10*x^2)*exp(3
)-10*x^4+10*x^3)*exp(x))/(((5*x^2*exp(3)-5*x^3)*exp(x)-9*x^2*exp(3)+9*x^3)*ln(-x+exp(3))^4+((20*x^3*exp(3)-20*
x^4)*exp(x)-36*x^3*exp(3)+36*x^4)*ln(-x+exp(3))^3+(((30*x^4-10*x^3)*exp(3)-30*x^5+10*x^4)*exp(x)+(-54*x^4+18*x
^3)*exp(3)+54*x^5-18*x^4)*ln(-x+exp(3))^2+(((20*x^5-20*x^4)*exp(3)-20*x^6+20*x^5)*exp(x)+(-36*x^5+36*x^4)*exp(
3)+36*x^6-36*x^5)*ln(-x+exp(3))+((5*x^6-10*x^5+5*x^4)*exp(3)-5*x^7+10*x^6-5*x^5)*exp(x)+(-9*x^6+18*x^5-9*x^4)*
exp(3)+9*x^7-18*x^6+9*x^5),x,method=_RETURNVERBOSE)

[Out]

2/x/(x^2+2*x*ln(-x+exp(3))+ln(-x+exp(3))^2-x)*ln(5*exp(x)-9)

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maxima [A]  time = 0.60, size = 43, normalized size = 1.30 \begin {gather*} \frac {2 \, \log \left (5 \, e^{x} - 9\right )}{x^{3} + 2 \, x^{2} \log \left (-x + e^{3}\right ) + x \log \left (-x + e^{3}\right )^{2} - x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*log(-x+exp(3))^2+((-40*x*exp(3)+40*x^2+20*x)*exp(x)+72*x
*exp(3)-72*x^2-36*x)*log(-x+exp(3))+((-30*x^2+20*x)*exp(3)+30*x^3)*exp(x)+(54*x^2-36*x)*exp(3)-54*x^3)*log(5*e
xp(x)-9)+(10*x*exp(3)-10*x^2)*exp(x)*log(-x+exp(3))^2+(20*x^2*exp(3)-20*x^3)*exp(x)*log(-x+exp(3))+((10*x^3-10
*x^2)*exp(3)-10*x^4+10*x^3)*exp(x))/(((5*x^2*exp(3)-5*x^3)*exp(x)-9*x^2*exp(3)+9*x^3)*log(-x+exp(3))^4+((20*x^
3*exp(3)-20*x^4)*exp(x)-36*x^3*exp(3)+36*x^4)*log(-x+exp(3))^3+(((30*x^4-10*x^3)*exp(3)-30*x^5+10*x^4)*exp(x)+
(-54*x^4+18*x^3)*exp(3)+54*x^5-18*x^4)*log(-x+exp(3))^2+(((20*x^5-20*x^4)*exp(3)-20*x^6+20*x^5)*exp(x)+(-36*x^
5+36*x^4)*exp(3)+36*x^6-36*x^5)*log(-x+exp(3))+((5*x^6-10*x^5+5*x^4)*exp(3)-5*x^7+10*x^6-5*x^5)*exp(x)+(-9*x^6
+18*x^5-9*x^4)*exp(3)+9*x^7-18*x^6+9*x^5),x, algorithm="maxima")

[Out]

2*log(5*e^x - 9)/(x^3 + 2*x^2*log(-x + e^3) + x*log(-x + e^3)^2 - x^2)

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mupad [B]  time = 6.15, size = 40, normalized size = 1.21 \begin {gather*} \frac {2\,\ln \left (5\,{\mathrm {e}}^x-9\right )}{x\,\left (x^2+2\,x\,\ln \left ({\mathrm {e}}^3-x\right )-x+{\ln \left ({\mathrm {e}}^3-x\right )}^2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(5*exp(x) - 9)*(exp(3)*(36*x - 54*x^2) - exp(x)*(exp(3)*(20*x - 30*x^2) + 30*x^3) + 54*x^3 + log(exp(
3) - x)*(36*x - 72*x*exp(3) + 72*x^2 - exp(x)*(20*x - 40*x*exp(3) + 40*x^2)) - log(exp(3) - x)^2*(18*exp(3) -
18*x + exp(x)*(10*x - 10*exp(3)))) + exp(x)*(exp(3)*(10*x^2 - 10*x^3) - 10*x^3 + 10*x^4) - log(exp(3) - x)^2*e
xp(x)*(10*x*exp(3) - 10*x^2) - log(exp(3) - x)*exp(x)*(20*x^2*exp(3) - 20*x^3))/(exp(x)*(exp(3)*(5*x^4 - 10*x^
5 + 5*x^6) - 5*x^5 + 10*x^6 - 5*x^7) + log(exp(3) - x)*(exp(3)*(36*x^4 - 36*x^5) - exp(x)*(exp(3)*(20*x^4 - 20
*x^5) - 20*x^5 + 20*x^6) - 36*x^5 + 36*x^6) + log(exp(3) - x)^4*(exp(x)*(5*x^2*exp(3) - 5*x^3) - 9*x^2*exp(3)
+ 9*x^3) + log(exp(3) - x)^3*(exp(x)*(20*x^3*exp(3) - 20*x^4) - 36*x^3*exp(3) + 36*x^4) + log(exp(3) - x)^2*(e
xp(3)*(18*x^3 - 54*x^4) - exp(x)*(exp(3)*(10*x^3 - 30*x^4) - 10*x^4 + 30*x^5) - 18*x^4 + 54*x^5) - exp(3)*(9*x
^4 - 18*x^5 + 9*x^6) + 9*x^5 - 18*x^6 + 9*x^7),x)

[Out]

(2*log(5*exp(x) - 9))/(x*(log(exp(3) - x)^2 - x + x^2 + 2*x*log(exp(3) - x)))

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sympy [A]  time = 1.23, size = 37, normalized size = 1.12 \begin {gather*} \frac {2 \log {\left (5 e^{x} - 9 \right )}}{x^{3} + 2 x^{2} \log {\left (- x + e^{3} \right )} - x^{2} + x \log {\left (- x + e^{3} \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*ln(-x+exp(3))**2+((-40*x*exp(3)+40*x**2+20*x)*exp(x)+72*
x*exp(3)-72*x**2-36*x)*ln(-x+exp(3))+((-30*x**2+20*x)*exp(3)+30*x**3)*exp(x)+(54*x**2-36*x)*exp(3)-54*x**3)*ln
(5*exp(x)-9)+(10*x*exp(3)-10*x**2)*exp(x)*ln(-x+exp(3))**2+(20*x**2*exp(3)-20*x**3)*exp(x)*ln(-x+exp(3))+((10*
x**3-10*x**2)*exp(3)-10*x**4+10*x**3)*exp(x))/(((5*x**2*exp(3)-5*x**3)*exp(x)-9*x**2*exp(3)+9*x**3)*ln(-x+exp(
3))**4+((20*x**3*exp(3)-20*x**4)*exp(x)-36*x**3*exp(3)+36*x**4)*ln(-x+exp(3))**3+(((30*x**4-10*x**3)*exp(3)-30
*x**5+10*x**4)*exp(x)+(-54*x**4+18*x**3)*exp(3)+54*x**5-18*x**4)*ln(-x+exp(3))**2+(((20*x**5-20*x**4)*exp(3)-2
0*x**6+20*x**5)*exp(x)+(-36*x**5+36*x**4)*exp(3)+36*x**6-36*x**5)*ln(-x+exp(3))+((5*x**6-10*x**5+5*x**4)*exp(3
)-5*x**7+10*x**6-5*x**5)*exp(x)+(-9*x**6+18*x**5-9*x**4)*exp(3)+9*x**7-18*x**6+9*x**5),x)

[Out]

2*log(5*exp(x) - 9)/(x**3 + 2*x**2*log(-x + exp(3)) - x**2 + x*log(-x + exp(3))**2)

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