3.71.65 \(\int \frac {-e^{2 x}+3 x-3 x^2-3 e^x \log (4)+(e (3-6 x)-3 x+6 x^2+e^{2 x} (-2 e+2 x)+e^x (-3 e+3 x) \log (4)) \log (e-x)}{e^{4 x} (e-x)-9 x^3+18 x^4-9 x^5+e (9 x^2-18 x^3+9 x^4)+e^{3 x} (6 e-6 x) \log (4)+e^x (18 x^2-18 x^3+e (-18 x+18 x^2)) \log (4)+e^{2 x} (6 x^2-6 x^3+e (-6 x+6 x^2)+(9 e-9 x) \log ^2(4))} \, dx\)

Optimal. Leaf size=30 \[ \frac {\log (e-x)}{e^{2 x}+3 \left (-x+x^2+e^x \log (4)\right )} \]

________________________________________________________________________________________

Rubi [F]  time = 4.53, 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^{2 x}+3 x-3 x^2-3 e^x \log (4)+\left (e (3-6 x)-3 x+6 x^2+e^{2 x} (-2 e+2 x)+e^x (-3 e+3 x) \log (4)\right ) \log (e-x)}{e^{4 x} (e-x)-9 x^3+18 x^4-9 x^5+e \left (9 x^2-18 x^3+9 x^4\right )+e^{3 x} (6 e-6 x) \log (4)+e^x \left (18 x^2-18 x^3+e \left (-18 x+18 x^2\right )\right ) \log (4)+e^{2 x} \left (6 x^2-6 x^3+e \left (-6 x+6 x^2\right )+(9 e-9 x) \log ^2(4)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-E^(2*x) + 3*x - 3*x^2 - 3*E^x*Log[4] + (E*(3 - 6*x) - 3*x + 6*x^2 + E^(2*x)*(-2*E + 2*x) + E^x*(-3*E + 3
*x)*Log[4])*Log[E - x])/(E^(4*x)*(E - x) - 9*x^3 + 18*x^4 - 9*x^5 + E*(9*x^2 - 18*x^3 + 9*x^4) + E^(3*x)*(6*E
- 6*x)*Log[4] + E^x*(18*x^2 - 18*x^3 + E*(-18*x + 18*x^2))*Log[4] + E^(2*x)*(6*x^2 - 6*x^3 + E*(-6*x + 6*x^2)
+ (9*E - 9*x)*Log[4]^2)),x]

[Out]

3*Log[E - x]*Defer[Int][(E^(2*x) - 3*x + 3*x^2 + E^x*Log[64])^(-2), x] + Log[64]*Log[E - x]*Defer[Int][E^x/(E^
(2*x) - 3*x + 3*x^2 + E^x*Log[64])^2, x] - 12*Log[E - x]*Defer[Int][x/(E^(2*x) - 3*x + 3*x^2 + E^x*Log[64])^2,
x] + 6*Log[E - x]*Defer[Int][x^2/(E^(2*x) - 3*x + 3*x^2 + E^x*Log[64])^2, x] - 2*Log[E - x]*Defer[Int][(E^(2*
x) - 3*x + 3*x^2 + E^x*Log[64])^(-1), x] - Defer[Int][1/((E - x)*(E^(2*x) - 3*x + 3*x^2 + E^x*Log[64])), x] +
3*Defer[Int][Defer[Int][(E^(2*x) + 3*(-1 + x)*x + E^x*Log[64])^(-2), x]/(E - x), x] + Log[64]*Defer[Int][Defer
[Int][E^x/(E^(2*x) + 3*(-1 + x)*x + E^x*Log[64])^2, x]/(E - x), x] - 12*Defer[Int][Defer[Int][x/(E^(2*x) + 3*(
-1 + x)*x + E^x*Log[64])^2, x]/(E - x), x] + 6*Defer[Int][Defer[Int][x^2/(E^(2*x) + 3*(-1 + x)*x + E^x*Log[64]
)^2, x]/(E - x), x] - 2*Defer[Int][Defer[Int][(E^(2*x) + 3*(-1 + x)*x + E^x*Log[64])^(-1), x]/(E - x), x] + 2*
E*Defer[Int][Defer[Int][1/((E - x)*(E^(2*x) + 3*(-1 + x)*x + E^x*Log[64])), x]/(E - x), x] + 2*E*Defer[Int][De
fer[Int][1/((E - x)*(E^(2*x) + 3*(-1 + x)*x + E^x*Log[64])), x]/(-E + x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^{2 x}-3 (-1+x) x-e^x \log (64)-(e-x) \left (-3+2 e^{2 x}+6 x+e^x \log (64)\right ) \log (e-x)}{(e-x) \left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx\\ &=\int \left (\frac {\left (3-12 x+6 x^2+e^x \log (64)\right ) \log (e-x)}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2}-\frac {1+2 e \log (e-x)-2 x \log (e-x)}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )}\right ) \, dx\\ &=\int \frac {\left (3-12 x+6 x^2+e^x \log (64)\right ) \log (e-x)}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-\int \frac {1+2 e \log (e-x)-2 x \log (e-x)}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )} \, dx\\ &=(3 \log (e-x)) \int \frac {1}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(6 \log (e-x)) \int \frac {x^2}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-(12 \log (e-x)) \int \frac {x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(\log (64) \log (e-x)) \int \frac {e^x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-\int \left (\frac {1}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )}+\frac {2 e \log (e-x)}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )}-\frac {2 x \log (e-x)}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )}\right ) \, dx-\int \frac {-3 \int \frac {1}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx-\log (64) \int \frac {e^x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx-6 \left (-2 \int \frac {x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx+\int \frac {x^2}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx\right )}{e-x} \, dx\\ &=2 \int \frac {x \log (e-x)}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )} \, dx-(2 e) \int \frac {\log (e-x)}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )} \, dx+(3 \log (e-x)) \int \frac {1}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(6 \log (e-x)) \int \frac {x^2}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-(12 \log (e-x)) \int \frac {x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(\log (64) \log (e-x)) \int \frac {e^x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-\int \frac {1}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )} \, dx-\int \left (\frac {-3 \int \frac {1}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx-\log (64) \int \frac {e^x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx+12 \int \frac {x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x}-\frac {6 \int \frac {x^2}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x}\right ) \, dx\\ &=-\left (2 \int \frac {\int \frac {1}{e^{2 x}+3 (-1+x) x+e^x \log (64)} \, dx-e \int \frac {1}{(e-x) \left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )} \, dx}{e-x} \, dx\right )+6 \int \frac {\int \frac {x^2}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx+(2 e) \int \frac {\int \frac {1}{(e-x) \left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )} \, dx}{-e+x} \, dx-(2 \log (e-x)) \int \frac {1}{e^{2 x}-3 x+3 x^2+e^x \log (64)} \, dx+(3 \log (e-x)) \int \frac {1}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(6 \log (e-x)) \int \frac {x^2}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-(12 \log (e-x)) \int \frac {x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(\log (64) \log (e-x)) \int \frac {e^x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-\int \frac {1}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )} \, dx-\int \frac {-3 \int \frac {1}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx-\log (64) \int \frac {e^x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx+12 \int \frac {x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx\\ &=-\left (2 \int \left (\frac {\int \frac {1}{e^{2 x}+3 (-1+x) x+e^x \log (64)} \, dx}{e-x}-\frac {e \int \frac {1}{(e-x) \left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )} \, dx}{e-x}\right ) \, dx\right )+6 \int \frac {\int \frac {x^2}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx+(2 e) \int \frac {\int \frac {1}{(e-x) \left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )} \, dx}{-e+x} \, dx-(2 \log (e-x)) \int \frac {1}{e^{2 x}-3 x+3 x^2+e^x \log (64)} \, dx+(3 \log (e-x)) \int \frac {1}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(6 \log (e-x)) \int \frac {x^2}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-(12 \log (e-x)) \int \frac {x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(\log (64) \log (e-x)) \int \frac {e^x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-\int \frac {1}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )} \, dx-\int \left (\frac {-3 \int \frac {1}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx-\log (64) \int \frac {e^x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x}+\frac {12 \int \frac {x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x}\right ) \, dx\\ &=-\left (2 \int \frac {\int \frac {1}{e^{2 x}+3 (-1+x) x+e^x \log (64)} \, dx}{e-x} \, dx\right )+6 \int \frac {\int \frac {x^2}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx-12 \int \frac {\int \frac {x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx+(2 e) \int \frac {\int \frac {1}{(e-x) \left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )} \, dx}{e-x} \, dx+(2 e) \int \frac {\int \frac {1}{(e-x) \left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )} \, dx}{-e+x} \, dx-(2 \log (e-x)) \int \frac {1}{e^{2 x}-3 x+3 x^2+e^x \log (64)} \, dx+(3 \log (e-x)) \int \frac {1}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(6 \log (e-x)) \int \frac {x^2}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-(12 \log (e-x)) \int \frac {x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(\log (64) \log (e-x)) \int \frac {e^x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-\int \frac {1}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )} \, dx-\int \frac {-3 \int \frac {1}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx-\log (64) \int \frac {e^x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx\\ &=-\left (2 \int \frac {\int \frac {1}{e^{2 x}+3 (-1+x) x+e^x \log (64)} \, dx}{e-x} \, dx\right )+6 \int \frac {\int \frac {x^2}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx-12 \int \frac {\int \frac {x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx+(2 e) \int \frac {\int \frac {1}{(e-x) \left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )} \, dx}{e-x} \, dx+(2 e) \int \frac {\int \frac {1}{(e-x) \left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )} \, dx}{-e+x} \, dx-(2 \log (e-x)) \int \frac {1}{e^{2 x}-3 x+3 x^2+e^x \log (64)} \, dx+(3 \log (e-x)) \int \frac {1}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(6 \log (e-x)) \int \frac {x^2}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-(12 \log (e-x)) \int \frac {x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(\log (64) \log (e-x)) \int \frac {e^x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-\int \frac {1}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )} \, dx-\int \left (-\frac {3 \int \frac {1}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x}-\frac {\log (64) \int \frac {e^x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x}\right ) \, dx\\ &=-\left (2 \int \frac {\int \frac {1}{e^{2 x}+3 (-1+x) x+e^x \log (64)} \, dx}{e-x} \, dx\right )+3 \int \frac {\int \frac {1}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx+6 \int \frac {\int \frac {x^2}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx-12 \int \frac {\int \frac {x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx+(2 e) \int \frac {\int \frac {1}{(e-x) \left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )} \, dx}{e-x} \, dx+(2 e) \int \frac {\int \frac {1}{(e-x) \left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )} \, dx}{-e+x} \, dx+\log (64) \int \frac {\int \frac {e^x}{\left (e^{2 x}+3 (-1+x) x+e^x \log (64)\right )^2} \, dx}{e-x} \, dx-(2 \log (e-x)) \int \frac {1}{e^{2 x}-3 x+3 x^2+e^x \log (64)} \, dx+(3 \log (e-x)) \int \frac {1}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(6 \log (e-x)) \int \frac {x^2}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-(12 \log (e-x)) \int \frac {x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx+(\log (64) \log (e-x)) \int \frac {e^x}{\left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )^2} \, dx-\int \frac {1}{(e-x) \left (e^{2 x}-3 x+3 x^2+e^x \log (64)\right )} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.88, size = 29, normalized size = 0.97 \begin {gather*} \frac {\log (e-x)}{e^{2 x}-3 x+3 x^2+e^x \log (64)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-E^(2*x) + 3*x - 3*x^2 - 3*E^x*Log[4] + (E*(3 - 6*x) - 3*x + 6*x^2 + E^(2*x)*(-2*E + 2*x) + E^x*(-3
*E + 3*x)*Log[4])*Log[E - x])/(E^(4*x)*(E - x) - 9*x^3 + 18*x^4 - 9*x^5 + E*(9*x^2 - 18*x^3 + 9*x^4) + E^(3*x)
*(6*E - 6*x)*Log[4] + E^x*(18*x^2 - 18*x^3 + E*(-18*x + 18*x^2))*Log[4] + E^(2*x)*(6*x^2 - 6*x^3 + E*(-6*x + 6
*x^2) + (9*E - 9*x)*Log[4]^2)),x]

[Out]

Log[E - x]/(E^(2*x) - 3*x + 3*x^2 + E^x*Log[64])

________________________________________________________________________________________

fricas [A]  time = 0.84, size = 29, normalized size = 0.97 \begin {gather*} \frac {\log \left (-x + e\right )}{3 \, x^{2} + 6 \, e^{x} \log \relax (2) - 3 \, x + e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*exp(1)+2*x)*exp(x)^2+2*(-3*exp(1)+3*x)*log(2)*exp(x)+(-6*x+3)*exp(1)+6*x^2-3*x)*log(exp(1)-x)-
exp(x)^2-6*exp(x)*log(2)-3*x^2+3*x)/((exp(1)-x)*exp(x)^4+2*(6*exp(1)-6*x)*log(2)*exp(x)^3+(4*(9*exp(1)-9*x)*lo
g(2)^2+(6*x^2-6*x)*exp(1)-6*x^3+6*x^2)*exp(x)^2+2*((18*x^2-18*x)*exp(1)-18*x^3+18*x^2)*log(2)*exp(x)+(9*x^4-18
*x^3+9*x^2)*exp(1)-9*x^5+18*x^4-9*x^3),x, algorithm="fricas")

[Out]

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

________________________________________________________________________________________

giac [A]  time = 0.57, size = 29, normalized size = 0.97 \begin {gather*} \frac {\log \left (-x + e\right )}{3 \, x^{2} + 6 \, e^{x} \log \relax (2) - 3 \, x + e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*exp(1)+2*x)*exp(x)^2+2*(-3*exp(1)+3*x)*log(2)*exp(x)+(-6*x+3)*exp(1)+6*x^2-3*x)*log(exp(1)-x)-
exp(x)^2-6*exp(x)*log(2)-3*x^2+3*x)/((exp(1)-x)*exp(x)^4+2*(6*exp(1)-6*x)*log(2)*exp(x)^3+(4*(9*exp(1)-9*x)*lo
g(2)^2+(6*x^2-6*x)*exp(1)-6*x^3+6*x^2)*exp(x)^2+2*((18*x^2-18*x)*exp(1)-18*x^3+18*x^2)*log(2)*exp(x)+(9*x^4-18
*x^3+9*x^2)*exp(1)-9*x^5+18*x^4-9*x^3),x, algorithm="giac")

[Out]

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

________________________________________________________________________________________

maple [A]  time = 0.06, size = 30, normalized size = 1.00

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-2*exp(1)+2*x)*exp(x)^2+2*(-3*exp(1)+3*x)*ln(2)*exp(x)+(-6*x+3)*exp(1)+6*x^2-3*x)*ln(exp(1)-x)-exp(x)^2
-6*exp(x)*ln(2)-3*x^2+3*x)/((exp(1)-x)*exp(x)^4+2*(6*exp(1)-6*x)*ln(2)*exp(x)^3+(4*(9*exp(1)-9*x)*ln(2)^2+(6*x
^2-6*x)*exp(1)-6*x^3+6*x^2)*exp(x)^2+2*((18*x^2-18*x)*exp(1)-18*x^3+18*x^2)*ln(2)*exp(x)+(9*x^4-18*x^3+9*x^2)*
exp(1)-9*x^5+18*x^4-9*x^3),x,method=_RETURNVERBOSE)

[Out]

ln(exp(1)-x)/(exp(2*x)+3*x^2+6*exp(x)*ln(2)-3*x)

________________________________________________________________________________________

maxima [A]  time = 0.68, size = 29, normalized size = 0.97 \begin {gather*} \frac {\log \left (-x + e\right )}{3 \, x^{2} + 6 \, e^{x} \log \relax (2) - 3 \, x + e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*exp(1)+2*x)*exp(x)^2+2*(-3*exp(1)+3*x)*log(2)*exp(x)+(-6*x+3)*exp(1)+6*x^2-3*x)*log(exp(1)-x)-
exp(x)^2-6*exp(x)*log(2)-3*x^2+3*x)/((exp(1)-x)*exp(x)^4+2*(6*exp(1)-6*x)*log(2)*exp(x)^3+(4*(9*exp(1)-9*x)*lo
g(2)^2+(6*x^2-6*x)*exp(1)-6*x^3+6*x^2)*exp(x)^2+2*((18*x^2-18*x)*exp(1)-18*x^3+18*x^2)*log(2)*exp(x)+(9*x^4-18
*x^3+9*x^2)*exp(1)-9*x^5+18*x^4-9*x^3),x, algorithm="maxima")

[Out]

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

________________________________________________________________________________________

mupad [B]  time = 5.17, size = 29, normalized size = 0.97 \begin {gather*} \frac {\ln \left (\mathrm {e}-x\right )}{{\mathrm {e}}^{2\,x}-3\,x+6\,{\mathrm {e}}^x\,\ln \relax (2)+3\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*x) - 3*x - log(exp(1) - x)*(exp(2*x)*(2*x - 2*exp(1)) - 3*x + 6*x^2 - exp(1)*(6*x - 3) + 2*exp(x)*l
og(2)*(3*x - 3*exp(1))) + 6*exp(x)*log(2) + 3*x^2)/(exp(4*x)*(x - exp(1)) + exp(2*x)*(4*log(2)^2*(9*x - 9*exp(
1)) + exp(1)*(6*x - 6*x^2) - 6*x^2 + 6*x^3) - exp(1)*(9*x^2 - 18*x^3 + 9*x^4) + 9*x^3 - 18*x^4 + 9*x^5 + 2*exp
(3*x)*log(2)*(6*x - 6*exp(1)) + 2*exp(x)*log(2)*(exp(1)*(18*x - 18*x^2) - 18*x^2 + 18*x^3)),x)

[Out]

log(exp(1) - x)/(exp(2*x) - 3*x + 6*exp(x)*log(2) + 3*x^2)

________________________________________________________________________________________

sympy [A]  time = 0.50, size = 27, normalized size = 0.90 \begin {gather*} \frac {\log {\left (e - x \right )}}{3 x^{2} - 3 x + e^{2 x} + 6 e^{x} \log {\relax (2 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*exp(1)+2*x)*exp(x)**2+2*(-3*exp(1)+3*x)*ln(2)*exp(x)+(-6*x+3)*exp(1)+6*x**2-3*x)*ln(exp(1)-x)-
exp(x)**2-6*exp(x)*ln(2)-3*x**2+3*x)/((exp(1)-x)*exp(x)**4+2*(6*exp(1)-6*x)*ln(2)*exp(x)**3+(4*(9*exp(1)-9*x)*
ln(2)**2+(6*x**2-6*x)*exp(1)-6*x**3+6*x**2)*exp(x)**2+2*((18*x**2-18*x)*exp(1)-18*x**3+18*x**2)*ln(2)*exp(x)+(
9*x**4-18*x**3+9*x**2)*exp(1)-9*x**5+18*x**4-9*x**3),x)

[Out]

log(E - x)/(3*x**2 - 3*x + exp(2*x) + 6*exp(x)*log(2))

________________________________________________________________________________________