3.70.34 \(\int \frac {-35 x+15 x^2-35 x \log (x)+e^{\frac {e^{e^6}}{x}} (-5 x+(-5 e^{e^6}-5 x) \log (x))}{49 x+e^{\frac {2 e^{e^6}}{x}} x-42 x^2+9 x^3+e^{\frac {e^{e^6}}{x}} (14 x-6 x^2)} \, dx\)

Optimal. Leaf size=27 \[ \frac {5 x \log (x)}{5-e^{\frac {e^{e^6}}{x}}+3 (-4+x)} \]

________________________________________________________________________________________

Rubi [F]  time = 3.30, 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 {-35 x+15 x^2-35 x \log (x)+e^{\frac {e^{e^6}}{x}} \left (-5 x+\left (-5 e^{e^6}-5 x\right ) \log (x)\right )}{49 x+e^{\frac {2 e^{e^6}}{x}} x-42 x^2+9 x^3+e^{\frac {e^{e^6}}{x}} \left (14 x-6 x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-35*x + 15*x^2 - 35*x*Log[x] + E^(E^E^6/x)*(-5*x + (-5*E^E^6 - 5*x)*Log[x]))/(49*x + E^((2*E^E^6)/x)*x -
42*x^2 + 9*x^3 + E^(E^E^6/x)*(14*x - 6*x^2)),x]

[Out]

-15*E^E^6*Log[x]*Defer[Int][(7 + E^(E^E^6/x) - 3*x)^(-2), x] - 5*Defer[Int][(7 + E^(E^E^6/x) - 3*x)^(-1), x] -
5*Log[x]*Defer[Int][(7 + E^(E^E^6/x) - 3*x)^(-1), x] + 35*E^E^6*Log[x]*Defer[Int][1/((7 + E^(E^E^6/x) - 3*x)^
2*x), x] - 5*E^E^6*Log[x]*Defer[Int][1/((7 + E^(E^E^6/x) - 3*x)*x), x] - 15*Log[x]*Defer[Int][x/(7 + E^(E^E^6/
x) - 3*x)^2, x] + 15*E^E^6*Defer[Int][Defer[Int][(7 + E^(E^E^6/x) - 3*x)^(-2), x]/x, x] + 5*Defer[Int][Defer[I
nt][(7 + E^(E^E^6/x) - 3*x)^(-1), x]/x, x] - 35*E^E^6*Defer[Int][Defer[Int][1/((7 + E^(E^E^6/x) - 3*x)^2*x), x
]/x, x] + 5*E^E^6*Defer[Int][Defer[Int][1/((7 + E^(E^E^6/x) - 3*x)*x), x]/x, x] + 15*Defer[Int][Defer[Int][x/(
7 + E^(E^E^6/x) - 3*x)^2, x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-35 x+15 x^2-35 x \log (x)+e^{\frac {e^{e^6}}{x}} \left (-5 x+\left (-5 e^{e^6}-5 x\right ) \log (x)\right )}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx\\ &=\int \left (-\frac {5 \left (-7 e^{e^6}+3 e^{e^6} x+3 x^2\right ) \log (x)}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x}-\frac {5 \left (x+e^{e^6} \log (x)+x \log (x)\right )}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right ) x}\right ) \, dx\\ &=-\left (5 \int \frac {\left (-7 e^{e^6}+3 e^{e^6} x+3 x^2\right ) \log (x)}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx\right )-5 \int \frac {x+e^{e^6} \log (x)+x \log (x)}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right ) x} \, dx\\ &=-\left (5 \int \left (\frac {1}{7+e^{\frac {e^{e^6}}{x}}-3 x}+\frac {\log (x)}{7+e^{\frac {e^{e^6}}{x}}-3 x}+\frac {e^{e^6} \log (x)}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right ) x}\right ) \, dx\right )+5 \int \frac {3 e^{e^6} \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx-7 e^{e^6} \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx+3 \int \frac {x}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx}{x} \, dx-(15 \log (x)) \int \frac {x}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx-\left (15 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx+\left (35 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx\\ &=-\left (5 \int \frac {1}{7+e^{\frac {e^{e^6}}{x}}-3 x} \, dx\right )-5 \int \frac {\log (x)}{7+e^{\frac {e^{e^6}}{x}}-3 x} \, dx+5 \int \left (\frac {e^{e^6} \left (3 \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx-7 \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx\right )}{x}+\frac {3 \int \frac {x}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx}{x}\right ) \, dx-\left (5 e^{e^6}\right ) \int \frac {\log (x)}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right ) x} \, dx-(15 \log (x)) \int \frac {x}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx-\left (15 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx+\left (35 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx\\ &=-\left (5 \int \frac {1}{7+e^{\frac {e^{e^6}}{x}}-3 x} \, dx\right )+5 \int \frac {\int \frac {1}{7+e^{\frac {e^{e^6}}{x}}-3 x} \, dx}{x} \, dx+15 \int \frac {\int \frac {x}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx}{x} \, dx+\left (5 e^{e^6}\right ) \int \frac {3 \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx-7 \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx}{x} \, dx+\left (5 e^{e^6}\right ) \int \frac {\int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right ) x} \, dx}{x} \, dx-(5 \log (x)) \int \frac {1}{7+e^{\frac {e^{e^6}}{x}}-3 x} \, dx-(15 \log (x)) \int \frac {x}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx-\left (5 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right ) x} \, dx-\left (15 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx+\left (35 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx\\ &=-\left (5 \int \frac {1}{7+e^{\frac {e^{e^6}}{x}}-3 x} \, dx\right )+5 \int \frac {\int \frac {1}{7+e^{\frac {e^{e^6}}{x}}-3 x} \, dx}{x} \, dx+15 \int \frac {\int \frac {x}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx}{x} \, dx+\left (5 e^{e^6}\right ) \int \left (\frac {3 \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx}{x}-\frac {7 \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx}{x}\right ) \, dx+\left (5 e^{e^6}\right ) \int \frac {\int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right ) x} \, dx}{x} \, dx-(5 \log (x)) \int \frac {1}{7+e^{\frac {e^{e^6}}{x}}-3 x} \, dx-(15 \log (x)) \int \frac {x}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx-\left (5 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right ) x} \, dx-\left (15 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx+\left (35 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx\\ &=-\left (5 \int \frac {1}{7+e^{\frac {e^{e^6}}{x}}-3 x} \, dx\right )+5 \int \frac {\int \frac {1}{7+e^{\frac {e^{e^6}}{x}}-3 x} \, dx}{x} \, dx+15 \int \frac {\int \frac {x}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx}{x} \, dx+\left (5 e^{e^6}\right ) \int \frac {\int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right ) x} \, dx}{x} \, dx+\left (15 e^{e^6}\right ) \int \frac {\int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx}{x} \, dx-\left (35 e^{e^6}\right ) \int \frac {\int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx}{x} \, dx-(5 \log (x)) \int \frac {1}{7+e^{\frac {e^{e^6}}{x}}-3 x} \, dx-(15 \log (x)) \int \frac {x}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx-\left (5 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right ) x} \, dx-\left (15 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2} \, dx+\left (35 e^{e^6} \log (x)\right ) \int \frac {1}{\left (7+e^{\frac {e^{e^6}}{x}}-3 x\right )^2 x} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.49, size = 23, normalized size = 0.85 \begin {gather*} -\frac {5 x \log (x)}{7+e^{\frac {e^{e^6}}{x}}-3 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-35*x + 15*x^2 - 35*x*Log[x] + E^(E^E^6/x)*(-5*x + (-5*E^E^6 - 5*x)*Log[x]))/(49*x + E^((2*E^E^6)/x
)*x - 42*x^2 + 9*x^3 + E^(E^E^6/x)*(14*x - 6*x^2)),x]

[Out]

(-5*x*Log[x])/(7 + E^(E^E^6/x) - 3*x)

________________________________________________________________________________________

fricas [A]  time = 0.83, size = 22, normalized size = 0.81 \begin {gather*} \frac {5 \, x \log \relax (x)}{3 \, x - e^{\left (\frac {e^{\left (e^{6}\right )}}{x}\right )} - 7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-5*exp(exp(6))-5*x)*log(x)-5*x)*exp(exp(exp(6))/x)-35*x*log(x)+15*x^2-35*x)/(x*exp(exp(exp(6))/x)
^2+(-6*x^2+14*x)*exp(exp(exp(6))/x)+9*x^3-42*x^2+49*x),x, algorithm="fricas")

[Out]

5*x*log(x)/(3*x - e^(e^(e^6)/x) - 7)

________________________________________________________________________________________

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((((-5*exp(exp(6))-5*x)*log(x)-5*x)*exp(exp(exp(6))/x)-35*x*log(x)+15*x^2-35*x)/(x*exp(exp(exp(6))/x)
^2+(-6*x^2+14*x)*exp(exp(exp(6))/x)+9*x^3-42*x^2+49*x),x, algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

maple [A]  time = 0.03, size = 23, normalized size = 0.85

method	result	size
risch	\(\frac {5 x \ln \relax (x )}{3 x -7-{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{6}}}{x}}}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-5*exp(exp(6))-5*x)*ln(x)-5*x)*exp(exp(exp(6))/x)-35*x*ln(x)+15*x^2-35*x)/(x*exp(exp(exp(6))/x)^2+(-6*x
^2+14*x)*exp(exp(exp(6))/x)+9*x^3-42*x^2+49*x),x,method=_RETURNVERBOSE)

[Out]

5*x/(3*x-7-exp(exp(exp(6))/x))*ln(x)

________________________________________________________________________________________

maxima [A]  time = 0.42, size = 22, normalized size = 0.81 \begin {gather*} \frac {5 \, x \log \relax (x)}{3 \, x - e^{\left (\frac {e^{\left (e^{6}\right )}}{x}\right )} - 7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-5*exp(exp(6))-5*x)*log(x)-5*x)*exp(exp(exp(6))/x)-35*x*log(x)+15*x^2-35*x)/(x*exp(exp(exp(6))/x)
^2+(-6*x^2+14*x)*exp(exp(exp(6))/x)+9*x^3-42*x^2+49*x),x, algorithm="maxima")

[Out]

5*x*log(x)/(3*x - e^(e^(e^6)/x) - 7)

________________________________________________________________________________________

mupad [B]  time = 4.57, size = 69, normalized size = 2.56 \begin {gather*} -\frac {5\,\left (3\,x^5\,\ln \relax (x)-7\,x^3\,{\mathrm {e}}^{{\mathrm {e}}^6}\,\ln \relax (x)+3\,x^4\,{\mathrm {e}}^{{\mathrm {e}}^6}\,\ln \relax (x)\right )}{\left (3\,x^4+3\,{\mathrm {e}}^{{\mathrm {e}}^6}\,x^3-7\,{\mathrm {e}}^{{\mathrm {e}}^6}\,x^2\right )\,\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^6}}{x}}-3\,x+7\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(35*x + exp(exp(exp(6))/x)*(5*x + log(x)*(5*x + 5*exp(exp(6)))) + 35*x*log(x) - 15*x^2)/(49*x + exp(exp(e
xp(6))/x)*(14*x - 6*x^2) + x*exp((2*exp(exp(6)))/x) - 42*x^2 + 9*x^3),x)

[Out]

-(5*(3*x^5*log(x) - 7*x^3*exp(exp(6))*log(x) + 3*x^4*exp(exp(6))*log(x)))/((3*x^3*exp(exp(6)) - 7*x^2*exp(exp(
6)) + 3*x^4)*(exp(exp(exp(6))/x) - 3*x + 7))

________________________________________________________________________________________

sympy [A]  time = 0.27, size = 20, normalized size = 0.74 \begin {gather*} - \frac {5 x \log {\relax (x )}}{- 3 x + e^{\frac {e^{e^{6}}}{x}} + 7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-5*exp(exp(6))-5*x)*ln(x)-5*x)*exp(exp(exp(6))/x)-35*x*ln(x)+15*x**2-35*x)/(x*exp(exp(exp(6))/x)*
*2+(-6*x**2+14*x)*exp(exp(exp(6))/x)+9*x**3-42*x**2+49*x),x)

[Out]

-5*x*log(x)/(-3*x + exp(exp(exp(6))/x) + 7)

________________________________________________________________________________________