3.41.84 $\int \frac{e^{\frac{1}{{\log }^4(2x^5-x^6+(2x-x^2)\log (36))}}(40x^4-24x^5+(8-8x)\log (36))}{(-2x^5+x^6+(-2x+x^2)\log (36)){\log }^5(2x^5-x^6+(2x-x^2)\log (36))}dx$

Optimal. Leaf size=18 $$e^{\frac{1}{{\log }^4((2-x)x(x^4+\log (36)))}}$$

________________________________________________________________________________________

Rubi [F]  time = 5.06, 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 = {} $$\begin{array}{c}\int \frac{e^{\frac{1}{{\log }^4(2x^5-x^6+(2x-x^2)\log (36))}}(40x^4-24x^5+(8-8x)\log (36))}{(-2x^5+x^6+(-2x+x^2)\log (36)){\log }^5(2x^5-x^6+(2x-x^2)\log (36))}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(E^Log[2*x^5 - x^6 + (2*x - x^2)*Log[36]]^(-4)*(40*x^4 - 24*x^5 + (8 - 8*x)*Log[36]))/((-2*x^5 + x^6 + (-2
*x + x^2)*Log[36])*Log[2*x^5 - x^6 + (2*x - x^2)*Log[36]]^5),x]

[Out]

-4*Defer[Int][E^Log[-((-2 + x)*x*(x^4 + Log[36]))]^(-4)/((-2 + x)*Log[-((-2 + x)*x*(x^4 + Log[36]))]^5), x] -
4*Defer[Int][E^Log[-((-2 + x)*x*(x^4 + Log[36]))]^(-4)/(x*Log[-((-2 + x)*x*(x^4 + Log[36]))]^5), x] + 4*Defer[
Int][E^Log[-((-2 + x)*x*(x^4 + Log[36]))]^(-4)/((-x + (-Log[36])^(1/4))*Log[-((-2 + x)*x*(x^4 + Log[36]))]^5),
x] - 4*Defer[Int][E^Log[-((-2 + x)*x*(x^4 + Log[36]))]^(-4)/((x + (-Log[36])^(1/4))*Log[-((-2 + x)*x*(x^4 + L
og[36]))]^5), x] + 4*Defer[Int][E^Log[-((-2 + x)*x*(x^4 + Log[36]))]^(-4)/((-x - (-1)^(3/4)*Log[36]^(1/4))*Log
[-((-2 + x)*x*(x^4 + Log[36]))]^5), x] - 4*Defer[Int][E^Log[-((-2 + x)*x*(x^4 + Log[36]))]^(-4)/((x - (-1)^(3/
4)*Log[36]^(1/4))*Log[-((-2 + x)*x*(x^4 + Log[36]))]^5), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{8e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}(-5x^4+3x^5-\log (36)+x\log (36))}{(2-x)x(x^4+\log (36)){\log }^5(-((-2+x)x(x^4+\log (36))))}dx\\ & =8\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}(-5x^4+3x^5-\log (36)+x\log (36))}{(2-x)x(x^4+\log (36)){\log }^5(-((-2+x)x(x^4+\log (36))))}dx\\ & =8\int (-\frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{2(-2+x){\log }^5(-((-2+x)x(x^4+\log (36))))}-\frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{2x{\log }^5(-((-2+x)x(x^4+\log (36))))}-\frac{2e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}{x}^3}{(x^4+\log (36)){\log }^5(-((-2+x)x(x^4+\log (36))))})dx\\ & =-(4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{(-2+x){\log }^5(-((-2+x)x(x^4+\log (36))))}dx)-4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{x{\log }^5(-((-2+x)x(x^4+\log (36))))}dx-16\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}{x}^3}{(x^4+\log (36)){\log }^5(-((-2+x)x(x^4+\log (36))))}dx\\ & =-(4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{(-2+x){\log }^5(-((-2+x)x(x^4+\log (36))))}dx)-4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{x{\log }^5(-((-2+x)x(x^4+\log (36))))}dx-16\int (\frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}x}{2(x^2-i\sqrt{\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))}+\frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}x}{2(x^2+i\sqrt{\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))})dx\\ & =-(4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{(-2+x){\log }^5(-((-2+x)x(x^4+\log (36))))}dx)-4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{x{\log }^5(-((-2+x)x(x^4+\log (36))))}dx-8\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}x}{(x^2-i\sqrt{\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))}dx-8\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}x}{(x^2+i\sqrt{\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))}dx\\ & =-(4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{(-2+x){\log }^5(-((-2+x)x(x^4+\log (36))))}dx)-4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{x{\log }^5(-((-2+x)x(x^4+\log (36))))}dx-8\int (-\frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{2(-x+\sqrt[4]{-\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))}+\frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{2(x+\sqrt[4]{-\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))})dx-8\int (-\frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{2(-x-(-1{)}^{3/4}\sqrt[4]{\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))}+\frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{2(x-(-1{)}^{3/4}\sqrt[4]{\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))})dx\\ & =-(4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{(-2+x){\log }^5(-((-2+x)x(x^4+\log (36))))}dx)-4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{x{\log }^5(-((-2+x)x(x^4+\log (36))))}dx+4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{(-x+\sqrt[4]{-\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))}dx-4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{(x+\sqrt[4]{-\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))}dx+4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{(-x-(-1{)}^{3/4}\sqrt[4]{\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))}dx-4\int \frac{e^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}}{(x-(-1{)}^{3/4}\sqrt[4]{\log (36)}){\log }^5(-((-2+x)x(x^4+\log (36))))}dx\end{array}\end{array}$$

________________________________________________________________________________________

Mathematica [A]  time = 0.88, size = 17, normalized size = 0.94 $$\begin{array}{c}{e}^{\frac{1}{{\log }^4(-((-2+x)x(x^4+\log (36))))}}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^Log[2*x^5 - x^6 + (2*x - x^2)*Log[36]]^(-4)*(40*x^4 - 24*x^5 + (8 - 8*x)*Log[36]))/((-2*x^5 + x^6
+ (-2*x + x^2)*Log[36])*Log[2*x^5 - x^6 + (2*x - x^2)*Log[36]]^5),x]

[Out]

E^Log[-((-2 + x)*x*(x^4 + Log[36]))]^(-4)

________________________________________________________________________________________

fricas [A]  time = 0.55, size = 26, normalized size = 1.44 $$\begin{array}{c}{e}^{\left(\frac{1}{\log {(-x^6+2x^5-2(x^2-2x)\log (6))}^4}\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(-8*x+8)*log(6)-24*x^5+40*x^4)*exp(1/log(2*(-x^2+2*x)*log(6)-x^6+2*x^5)^4)/(2*(x^2-2*x)*log(6)+x^
6-2*x^5)/log(2*(-x^2+2*x)*log(6)-x^6+2*x^5)^5,x, algorithm="fricas")

[Out]

e^(log(-x^6 + 2*x^5 - 2*(x^2 - 2*x)*log(6))^(-4))

________________________________________________________________________________________

giac [A]  time = 0.13, size = 27, normalized size = 1.50 $$\begin{array}{c}{e}^{\left(\frac{1}{\log {(-x^6+2x^5-2x^2\log (6)+4x\log (6))}^4}\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(-8*x+8)*log(6)-24*x^5+40*x^4)*exp(1/log(2*(-x^2+2*x)*log(6)-x^6+2*x^5)^4)/(2*(x^2-2*x)*log(6)+x^
6-2*x^5)/log(2*(-x^2+2*x)*log(6)-x^6+2*x^5)^5,x, algorithm="giac")

[Out]

e^(log(-x^6 + 2*x^5 - 2*x^2*log(6) + 4*x*log(6))^(-4))

________________________________________________________________________________________

maple [A]  time = 0.04, size = 32, normalized size = 1.78

method	result	size
risch	${\mathrm{e}}^{\frac{1}{\ln {(2(-x^2+2x)(\ln (2)+\ln (3))-x^6+2x^5)}^4}}$	$32$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*(-8*x+8)*ln(6)-24*x^5+40*x^4)*exp(1/ln(2*(-x^2+2*x)*ln(6)-x^6+2*x^5)^4)/(2*(x^2-2*x)*ln(6)+x^6-2*x^5)/l
n(2*(-x^2+2*x)*ln(6)-x^6+2*x^5)^5,x,method=_RETURNVERBOSE)

[Out]

exp(1/ln(2*(-x^2+2*x)*(ln(2)+ln(3))-x^6+2*x^5)^4)

________________________________________________________________________________________

maxima [B]  time = 0.76, size = 1148, normalized size = 63.78 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(-8*x+8)*log(6)-24*x^5+40*x^4)*exp(1/log(2*(-x^2+2*x)*log(6)-x^6+2*x^5)^4)/(2*(x^2-2*x)*log(6)+x^
6-2*x^5)/log(2*(-x^2+2*x)*log(6)-x^6+2*x^5)^5,x, algorithm="maxima")

[Out]

3*x^5*e^(1/(log(x^4 + 2*log(3) + 2*log(2))^4 + 4*(log(x^4 + 2*log(3) + 2*log(2)) + log(-x + 2))*log(x)^3 + log
(x)^4 + 4*log(x^4 + 2*log(3) + 2*log(2))^3*log(-x + 2) + 6*log(x^4 + 2*log(3) + 2*log(2))^2*log(-x + 2)^2 + 4*
log(x^4 + 2*log(3) + 2*log(2))*log(-x + 2)^3 + log(-x + 2)^4 + 6*(log(x^4 + 2*log(3) + 2*log(2))^2 + 2*log(x^4
+ 2*log(3) + 2*log(2))*log(-x + 2) + log(-x + 2)^2)*log(x)^2 + 4*(log(x^4 + 2*log(3) + 2*log(2))^3 + 3*log(x^
4 + 2*log(3) + 2*log(2))^2*log(-x + 2) + 3*log(x^4 + 2*log(3) + 2*log(2))*log(-x + 2)^2 + log(-x + 2)^3)*log(x
)))/(3*x^5 - 5*x^4 + 2*x*(log(3) + log(2)) - 2*log(3) - 2*log(2)) - 5*x^4*e^(1/(log(x^4 + 2*log(3) + 2*log(2))
^4 + 4*(log(x^4 + 2*log(3) + 2*log(2)) + log(-x + 2))*log(x)^3 + log(x)^4 + 4*log(x^4 + 2*log(3) + 2*log(2))^3
*log(-x + 2) + 6*log(x^4 + 2*log(3) + 2*log(2))^2*log(-x + 2)^2 + 4*log(x^4 + 2*log(3) + 2*log(2))*log(-x + 2)
^3 + log(-x + 2)^4 + 6*(log(x^4 + 2*log(3) + 2*log(2))^2 + 2*log(x^4 + 2*log(3) + 2*log(2))*log(-x + 2) + log(
-x + 2)^2)*log(x)^2 + 4*(log(x^4 + 2*log(3) + 2*log(2))^3 + 3*log(x^4 + 2*log(3) + 2*log(2))^2*log(-x + 2) + 3
*log(x^4 + 2*log(3) + 2*log(2))*log(-x + 2)^2 + log(-x + 2)^3)*log(x)))/(3*x^5 - 5*x^4 + 2*x*(log(3) + log(2))
- 2*log(3) - 2*log(2)) + 2*x*e^(1/(log(x^4 + 2*log(3) + 2*log(2))^4 + 4*(log(x^4 + 2*log(3) + 2*log(2)) + log
(-x + 2))*log(x)^3 + log(x)^4 + 4*log(x^4 + 2*log(3) + 2*log(2))^3*log(-x + 2) + 6*log(x^4 + 2*log(3) + 2*log(
2))^2*log(-x + 2)^2 + 4*log(x^4 + 2*log(3) + 2*log(2))*log(-x + 2)^3 + log(-x + 2)^4 + 6*(log(x^4 + 2*log(3) +
2*log(2))^2 + 2*log(x^4 + 2*log(3) + 2*log(2))*log(-x + 2) + log(-x + 2)^2)*log(x)^2 + 4*(log(x^4 + 2*log(3)
+ 2*log(2))^3 + 3*log(x^4 + 2*log(3) + 2*log(2))^2*log(-x + 2) + 3*log(x^4 + 2*log(3) + 2*log(2))*log(-x + 2)^
2 + log(-x + 2)^3)*log(x)))*log(6)/(3*x^5 - 5*x^4 + 2*x*(log(3) + log(2)) - 2*log(3) - 2*log(2)) - 2*e^(1/(log
(x^4 + 2*log(3) + 2*log(2))^4 + 4*(log(x^4 + 2*log(3) + 2*log(2)) + log(-x + 2))*log(x)^3 + log(x)^4 + 4*log(x
^4 + 2*log(3) + 2*log(2))^3*log(-x + 2) + 6*log(x^4 + 2*log(3) + 2*log(2))^2*log(-x + 2)^2 + 4*log(x^4 + 2*log
(3) + 2*log(2))*log(-x + 2)^3 + log(-x + 2)^4 + 6*(log(x^4 + 2*log(3) + 2*log(2))^2 + 2*log(x^4 + 2*log(3) + 2
*log(2))*log(-x + 2) + log(-x + 2)^2)*log(x)^2 + 4*(log(x^4 + 2*log(3) + 2*log(2))^3 + 3*log(x^4 + 2*log(3) +
2*log(2))^2*log(-x + 2) + 3*log(x^4 + 2*log(3) + 2*log(2))*log(-x + 2)^2 + log(-x + 2)^3)*log(x)))*log(6)/(3*x
^5 - 5*x^4 + 2*x*(log(3) + log(2)) - 2*log(3) - 2*log(2))

________________________________________________________________________________________

mupad [B]  time = 3.84, size = 27, normalized size = 1.50 $$\begin{array}{c}{\mathrm{e}}^{\frac{1}{{\ln (-x^6+2x^5-2\ln (6)x^2+4\ln (6)x)}^4}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(1/log(2*log(6)*(2*x - x^2) + 2*x^5 - x^6)^4)*(2*log(6)*(8*x - 8) - 40*x^4 + 24*x^5))/(log(2*log(6)*(2
*x - x^2) + 2*x^5 - x^6)^5*(2*log(6)*(2*x - x^2) + 2*x^5 - x^6)),x)

[Out]

exp(1/log(4*x*log(6) - 2*x^2*log(6) + 2*x^5 - x^6)^4)

________________________________________________________________________________________

sympy [A]  time = 0.65, size = 26, normalized size = 1.44 $$\begin{array}{c}{e}^{\frac{1}{\log {(-x^6+2x^5+(-2x^2+4x)\log (6))}^4}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(-8*x+8)*ln(6)-24*x**5+40*x**4)*exp(1/ln(2*(-x**2+2*x)*ln(6)-x**6+2*x**5)**4)/(2*(x**2-2*x)*ln(6)
+x**6-2*x**5)/ln(2*(-x**2+2*x)*ln(6)-x**6+2*x**5)**5,x)

[Out]

exp(log(-x**6 + 2*x**5 + (-2*x**2 + 4*x)*log(6))**(-4))

________________________________________________________________________________________