3.26.70 $\int \frac{e^{\frac{-15+5x}{(39x-8x^2-4x^3+x^4)\log (x)}}(-585+315x+20x^2-35x^3+5x^4+(-585+240x+140x^2-100x^3+15x^4)\log (x))}{(1521x^2-624x^3-248x^4+142x^5-8x^7+x^8){\log }^2(x)}dx$

Optimal. Leaf size=31 $$-e^{\frac{5}{x(3+x)(-4+\frac{1}{-3+x}+x)\log (x)}}+\log (2)$$

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Rubi [F]  time = 13.34, 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 = {} $$\begin{array}{c}\int \frac{\exp \left(\frac{-15+5x}{(39x-8x^2-4x^3+x^4)\log (x)}\right)(-585+315x+20x^2-35x^3+5x^4+(-585+240x+140x^2-100x^3+15x^4)\log (x))}{(1521x^2-624x^3-248x^4+142x^5-8x^7+x^8){\log }^2(x)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(E^((-15 + 5*x)/((39*x - 8*x^2 - 4*x^3 + x^4)*Log[x]))*(-585 + 315*x + 20*x^2 - 35*x^3 + 5*x^4 + (-585 + 2
40*x + 140*x^2 - 100*x^3 + 15*x^4)*Log[x]))/((1521*x^2 - 624*x^3 - 248*x^4 + 142*x^5 - 8*x^7 + x^8)*Log[x]^2),
x]

[Out]

((-220*I)/7267)*Sqrt[3]*Defer[Int][E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))/((7 + I*Sqrt[3] - 2*x)*
Log[x]^2), x] - (5*Defer[Int][E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))/(x^2*Log[x]^2), x])/13 + (25
*Defer[Int][E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))/(x*Log[x]^2), x])/507 - (10*Defer[Int][E^((-15
+ 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))/((3 + x)*Log[x]^2), x])/129 + (205*(3 - (7*I)*Sqrt[3])*Defer[Int]
[E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))/((-7 - I*Sqrt[3] + 2*x)*Log[x]^2), x])/21801 - ((220*I)/7
267)*Sqrt[3]*Defer[Int][E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))/((-7 + I*Sqrt[3] + 2*x)*Log[x]^2),
x] + (205*(3 + (7*I)*Sqrt[3])*Defer[Int][E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))/((-7 + I*Sqrt[3]
+ 2*x)*Log[x]^2), x])/21801 + (((170*I)/559)*Defer[Int][E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))/(
(7 + I*Sqrt[3] - 2*x)*Log[x]), x])/Sqrt[3] - (5*Defer[Int][E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))
/(x^2*Log[x]), x])/13 + (10*Defer[Int][E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))/((3 + x)^2*Log[x]),
x])/43 + (((170*I)/559)*Defer[Int][E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))/((-7 + I*Sqrt[3] + 2*x
)*Log[x]), x])/Sqrt[3] - (775*Defer[Int][E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))/((13 - 7*x + x^2)
^2*Log[x]), x])/559 + (185*Defer[Int][(E^((-15 + 5*x)/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))*x)/((13 - 7*x + x^2
)^2*Log[x]), x])/559

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}(-585+315x+20x^2-35x^3+5x^4+(-585+240x+140x^2-100x^3+15x^4)\log (x))}{x^2{(39-8x-4x^2+x^3)}^2{\log }^2(x)}dx\\ & =\int (\frac{5e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}(-3+x)}{x^2(3+x)(13-7x+x^2){\log }^2(x)}+\frac{5e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}(-117+48x+28x^2-20x^3+3x^4)}{x^2(3+x{)}^2{(13-7x+x^2)}^2\log (x)})dx\\ & =5\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}(-3+x)}{x^2(3+x)(13-7x+x^2){\log }^2(x)}dx+5\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}(-117+48x+28x^2-20x^3+3x^4)}{x^2(3+x{)}^2{(13-7x+x^2)}^2\log (x)}dx\\ & =5\int (-\frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{13x^2{\log }^2(x)}+\frac{5e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{507x{\log }^2(x)}-\frac{2e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{129(3+x){\log }^2(x)}+\frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}(-66+41x)}{7267(13-7x+x^2){\log }^2(x)})dx+5\int (-\frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{13x^2\log (x)}+\frac{2e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{43(3+x{)}^2\log (x)}+\frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}(-155+37x)}{559{(13-7x+x^2)}^2\log (x)}+\frac{17e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{559(13-7x+x^2)\log (x)})dx\\ & =\frac{5\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}(-66+41x)}{(13-7x+x^2){\log }^2(x)}dx}{7267}+\frac{5}{559}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}(-155+37x)}{{(13-7x+x^2)}^2\log (x)}dx+\frac{25}{507}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x{\log }^2(x)}dx-\frac{10}{129}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(3+x){\log }^2(x)}dx+\frac{85}{559}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(13-7x+x^2)\log (x)}dx+\frac{10}{43}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(3+x{)}^2\log (x)}dx-\frac{5}{13}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x^2{\log }^2(x)}dx-\frac{5}{13}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x^2\log (x)}dx\\ & =\frac{5\int (-\frac{66e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(13-7x+x^2){\log }^2(x)}+\frac{41e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}x}{(13-7x+x^2){\log }^2(x)})dx}{7267}+\frac{5}{559}\int (-\frac{155e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{{(13-7x+x^2)}^2\log (x)}+\frac{37e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}x}{{(13-7x+x^2)}^2\log (x)})dx+\frac{25}{507}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x{\log }^2(x)}dx-\frac{10}{129}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(3+x){\log }^2(x)}dx+\frac{85}{559}\int (\frac{2i{e}^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{\sqrt{3}(7+i\sqrt{3}-2x)\log (x)}+\frac{2i{e}^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{\sqrt{3}(-7+i\sqrt{3}+2x)\log (x)})dx+\frac{10}{43}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(3+x{)}^2\log (x)}dx-\frac{5}{13}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x^2{\log }^2(x)}dx-\frac{5}{13}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x^2\log (x)}dx\\ & =\frac{205\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}x}{(13-7x+x^2){\log }^2(x)}dx}{7267}-\frac{330\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(13-7x+x^2){\log }^2(x)}dx}{7267}+\frac{25}{507}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x{\log }^2(x)}dx-\frac{10}{129}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(3+x){\log }^2(x)}dx+\frac{10}{43}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(3+x{)}^2\log (x)}dx+\frac{185}{559}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}x}{{(13-7x+x^2)}^2\log (x)}dx-\frac{5}{13}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x^2{\log }^2(x)}dx-\frac{5}{13}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x^2\log (x)}dx-\frac{775}{559}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{{(13-7x+x^2)}^2\log (x)}dx+\frac{(170i)\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(7+i\sqrt{3}-2x)\log (x)}dx}{559\sqrt{3}}+\frac{(170i)\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(-7+i\sqrt{3}+2x)\log (x)}dx}{559\sqrt{3}}\\ & =\frac{205\int (\frac{(1-\frac{7i}{\sqrt{3}})e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(-7-i\sqrt{3}+2x){\log }^2(x)}+\frac{(1+\frac{7i}{\sqrt{3}})e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(-7+i\sqrt{3}+2x){\log }^2(x)})dx}{7267}-\frac{330\int (\frac{2i{e}^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{\sqrt{3}(7+i\sqrt{3}-2x){\log }^2(x)}+\frac{2i{e}^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{\sqrt{3}(-7+i\sqrt{3}+2x){\log }^2(x)})dx}{7267}+\frac{25}{507}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x{\log }^2(x)}dx-\frac{10}{129}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(3+x){\log }^2(x)}dx+\frac{10}{43}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(3+x{)}^2\log (x)}dx+\frac{185}{559}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}x}{{(13-7x+x^2)}^2\log (x)}dx-\frac{5}{13}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x^2{\log }^2(x)}dx-\frac{5}{13}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x^2\log (x)}dx-\frac{775}{559}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{{(13-7x+x^2)}^2\log (x)}dx+\frac{(170i)\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(7+i\sqrt{3}-2x)\log (x)}dx}{559\sqrt{3}}+\frac{(170i)\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(-7+i\sqrt{3}+2x)\log (x)}dx}{559\sqrt{3}}\\ & =\frac{25}{507}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x{\log }^2(x)}dx-\frac{10}{129}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(3+x){\log }^2(x)}dx+\frac{10}{43}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(3+x{)}^2\log (x)}dx+\frac{185}{559}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}x}{{(13-7x+x^2)}^2\log (x)}dx-\frac{5}{13}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x^2{\log }^2(x)}dx-\frac{5}{13}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{x^2\log (x)}dx-\frac{775}{559}\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{{(13-7x+x^2)}^2\log (x)}dx+\frac{(170i)\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(7+i\sqrt{3}-2x)\log (x)}dx}{559\sqrt{3}}+\frac{(170i)\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(-7+i\sqrt{3}+2x)\log (x)}dx}{559\sqrt{3}}-\frac{\left(220i\sqrt{3}\right)\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(7+i\sqrt{3}-2x){\log }^2(x)}dx}{7267}-\frac{\left(220i\sqrt{3}\right)\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(-7+i\sqrt{3}+2x){\log }^2(x)}dx}{7267}+\frac{\left(205(3-7i\sqrt{3})\right)\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(-7-i\sqrt{3}+2x){\log }^2(x)}dx}{21801}+\frac{\left(205(3+7i\sqrt{3})\right)\int \frac{e^{\frac{-15+5x}{x(39-8x-4x^2+x^3)\log (x)}}}{(-7+i\sqrt{3}+2x){\log }^2(x)}dx}{21801}\end{array}\end{array}$$

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Mathematica [A]  time = 0.07, size = 31, normalized size = 1.00 $$\begin{array}{c}-e^{\frac{5(-3+x)}{x(39-8x-4x^2+x^3)\log (x)}}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^((-15 + 5*x)/((39*x - 8*x^2 - 4*x^3 + x^4)*Log[x]))*(-585 + 315*x + 20*x^2 - 35*x^3 + 5*x^4 + (-5
85 + 240*x + 140*x^2 - 100*x^3 + 15*x^4)*Log[x]))/((1521*x^2 - 624*x^3 - 248*x^4 + 142*x^5 - 8*x^7 + x^8)*Log[
x]^2),x]

[Out]

-E^((5*(-3 + x))/(x*(39 - 8*x - 4*x^2 + x^3)*Log[x]))

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fricas [A]  time = 0.85, size = 31, normalized size = 1.00 $$\begin{array}{c}-e^{\left(\frac{5(x-3)}{(x^4-4x^3-8x^2+39x)\log (x)}\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^4-100*x^3+140*x^2+240*x-585)*log(x)+5*x^4-35*x^3+20*x^2+315*x-585)*exp((5*x-15)/(x^4-4*x^3-8*
x^2+39*x)/log(x))/(x^8-8*x^7+142*x^5-248*x^4-624*x^3+1521*x^2)/log(x)^2,x, algorithm="fricas")

[Out]

-e^(5*(x - 3)/((x^4 - 4*x^3 - 8*x^2 + 39*x)*log(x)))

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giac [B]  time = 0.55, size = 65, normalized size = 2.10 $$\begin{array}{c}-e^{(\frac{5x}{x^4\log (x)-4x^3\log (x)-8x^2\log (x)+39x\log (x)}-\frac{15}{x^4\log (x)-4x^3\log (x)-8x^2\log (x)+39x\log (x)})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^4-100*x^3+140*x^2+240*x-585)*log(x)+5*x^4-35*x^3+20*x^2+315*x-585)*exp((5*x-15)/(x^4-4*x^3-8*
x^2+39*x)/log(x))/(x^8-8*x^7+142*x^5-248*x^4-624*x^3+1521*x^2)/log(x)^2,x, algorithm="giac")

[Out]

-e^(5*x/(x^4*log(x) - 4*x^3*log(x) - 8*x^2*log(x) + 39*x*log(x)) - 15/(x^4*log(x) - 4*x^3*log(x) - 8*x^2*log(x
) + 39*x*log(x)))

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maple [A]  time = 0.03, size = 31, normalized size = 1.00

method	result	size
risch	$-{\mathrm{e}}^{\frac{5x-15}{x(3+x)(x^2-7x+13)\ln (x)}}$	$31$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((15*x^4-100*x^3+140*x^2+240*x-585)*ln(x)+5*x^4-35*x^3+20*x^2+315*x-585)*exp((5*x-15)/(x^4-4*x^3-8*x^2+39*
x)/ln(x))/(x^8-8*x^7+142*x^5-248*x^4-624*x^3+1521*x^2)/ln(x)^2,x,method=_RETURNVERBOSE)

[Out]

-exp(5*(x-3)/x/(3+x)/(x^2-7*x+13)/ln(x))

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maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\text{Exception raised: RuntimeError}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^4-100*x^3+140*x^2+240*x-585)*log(x)+5*x^4-35*x^3+20*x^2+315*x-585)*exp((5*x-15)/(x^4-4*x^3-8*
x^2+39*x)/log(x))/(x^8-8*x^7+142*x^5-248*x^4-624*x^3+1521*x^2)/log(x)^2,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not
of the expected type LIST

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mupad [B]  time = 1.78, size = 62, normalized size = 2.00 $$\begin{array}{c}-{\mathrm{e}}^{\frac{15}{8x^2\ln (x)+4x^3\ln (x)-x^4\ln (x)-39x\ln (x)}}{\mathrm{e}}^{\frac{5}{39\ln (x)-4x^2\ln (x)+x^3\ln (x)-8x\ln (x)}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((5*x - 15)/(log(x)*(39*x - 8*x^2 - 4*x^3 + x^4)))*(315*x + log(x)*(240*x + 140*x^2 - 100*x^3 + 15*x^4
- 585) + 20*x^2 - 35*x^3 + 5*x^4 - 585))/(log(x)^2*(1521*x^2 - 624*x^3 - 248*x^4 + 142*x^5 - 8*x^7 + x^8)),x)

[Out]

-exp(15/(8*x^2*log(x) + 4*x^3*log(x) - x^4*log(x) - 39*x*log(x)))*exp(5/(39*log(x) - 4*x^2*log(x) + x^3*log(x)
- 8*x*log(x)))

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sympy [A]  time = 0.85, size = 27, normalized size = 0.87 $$\begin{array}{c}-e^{\frac{5x-15}{(x^4-4x^3-8x^2+39x)\log (x)}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x**4-100*x**3+140*x**2+240*x-585)*ln(x)+5*x**4-35*x**3+20*x**2+315*x-585)*exp((5*x-15)/(x**4-4*
x**3-8*x**2+39*x)/ln(x))/(x**8-8*x**7+142*x**5-248*x**4-624*x**3+1521*x**2)/ln(x)**2,x)

[Out]

-exp((5*x - 15)/((x**4 - 4*x**3 - 8*x**2 + 39*x)*log(x)))

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