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

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

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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 {gather*} \int \frac {\exp \left (\frac {-15+5 x}{\left (39 x-8 x^2-4 x^3+x^4\right ) \log (x)}\right ) \left (-585+315 x+20 x^2-35 x^3+5 x^4+\left (-585+240 x+140 x^2-100 x^3+15 x^4\right ) \log (x)\right )}{\left (1521 x^2-624 x^3-248 x^4+142 x^5-8 x^7+x^8\right ) \log ^2(x)} \, dx \end {gather*}

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

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

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 {gather*} -e^{\left (\frac {5 \, {\left (x - 3\right )}}{{\left (x^{4} - 4 \, x^{3} - 8 \, x^{2} + 39 \, x\right )} \log \relax (x)}\right )} \end {gather*}

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 {gather*} -e^{\left (\frac {5 \, x}{x^{4} \log \relax (x) - 4 \, x^{3} \log \relax (x) - 8 \, x^{2} \log \relax (x) + 39 \, x \log \relax (x)} - \frac {15}{x^{4} \log \relax (x) - 4 \, x^{3} \log \relax (x) - 8 \, x^{2} \log \relax (x) + 39 \, x \log \relax (x)}\right )} \end {gather*}

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	\(-{\mathrm e}^{\frac {5 x -15}{x \left (3+x \right ) \left (x^{2}-7 x +13\right ) \ln \relax (x )}}\)	\(31\)

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 {gather*} \text {Exception raised: RuntimeError} \end {gather*}

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 {gather*} -{\mathrm {e}}^{\frac {15}{8\,x^2\,\ln \relax (x)+4\,x^3\,\ln \relax (x)-x^4\,\ln \relax (x)-39\,x\,\ln \relax (x)}}\,{\mathrm {e}}^{\frac {5}{39\,\ln \relax (x)-4\,x^2\,\ln \relax (x)+x^3\,\ln \relax (x)-8\,x\,\ln \relax (x)}} \end {gather*}

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 {gather*} - e^{\frac {5 x - 15}{\left (x^{4} - 4 x^{3} - 8 x^{2} + 39 x\right ) \log {\relax (x )}}} \end {gather*}

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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