3.28.26 \(\int \frac {12 x+e^{15} (-4+4 x)+e^5 (-12+12 x-8 x^2)+e^{10} (12 x-8 x^2)+(-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 (24 x-16 x^2)) \log (x)+(12 x-8 x^2+e^5 (-12+12 x)) \log ^2(x)+(-4+4 x) \log ^3(x)}{(10 x+e^{20} x-12 e^5 x^2-4 e^{15} x^2+e^{10} (6 x+4 x^3)+(4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 (12 x+8 x^3)) \log (x)+(6 x+6 e^{10} x-12 e^5 x^2+4 x^3) \log ^2(x)+(4 e^5 x-4 x^2) \log ^3(x)+x \log ^4(x)) \log (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} (6+4 x^2)+(4 e^{15}-12 x-12 e^{10} x+e^5 (12+8 x^2)) \log (x)+(6+6 e^{10}-12 e^5 x+4 x^2) \log ^2(x)+(4 e^5-4 x) \log ^3(x)+\log ^4(x))} \, dx\)
Optimal. Leaf size=32 \[ \log \left (\frac {1}{e \log \left (1+\left (3-x^2+\left (-e^5+x-\log (x)\right )^2\right )^2\right )}\right ) \]
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Rubi [F] time = 19.60, 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 {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (10 x+e^{20} x-12 e^5 x^2-4 e^{15} x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(12*x + E^15*(-4 + 4*x) + E^5*(-12 + 12*x - 8*x^2) + E^10*(12*x - 8*x^2) + (-12 + 12*x - 8*x^2 + E^10*(-12
+ 12*x) + E^5*(24*x - 16*x^2))*Log[x] + (12*x - 8*x^2 + E^5*(-12 + 12*x))*Log[x]^2 + (-4 + 4*x)*Log[x]^3)/((1
0*x + E^20*x - 12*E^5*x^2 - 4*E^15*x^2 + E^10*(6*x + 4*x^3) + (4*E^15*x - 12*x^2 - 12*E^10*x^2 + E^5*(12*x + 8
*x^3))*Log[x] + (6*x + 6*E^10*x - 12*E^5*x^2 + 4*x^3)*Log[x]^2 + (4*E^5*x - 4*x^2)*Log[x]^3 + x*Log[x]^4)*Log[
10 + E^20 - 12*E^5*x - 4*E^15*x + E^10*(6 + 4*x^2) + (4*E^15 - 12*x - 12*E^10*x + E^5*(12 + 8*x^2))*Log[x] + (
6 + 6*E^10 - 12*E^5*x + 4*x^2)*Log[x]^2 + (4*E^5 - 4*x)*Log[x]^3 + Log[x]^4]),x]
[Out]
4*E^5*(3 + E^10)*Defer[Int][1/(x*(-10*(1 + (E^10*(6 + E^10))/10) + 12*E^5*(1 + E^10/3)*x - 4*E^10*x^2 - 12*E^5
*(1 + E^10/3)*Log[x] + 12*(1 + E^10)*x*Log[x] - 8*E^5*x^2*Log[x] - 6*(1 + E^10)*Log[x]^2 + 12*E^5*x*Log[x]^2 -
4*x^2*Log[x]^2 - 4*E^5*Log[x]^3 + 4*x*Log[x]^3 - Log[x]^4)*Log[10*(1 + E^20/10) - 4*E^5*(3 + E^10)*x + E^10*(
6 + 4*x^2) + 4*(E^15 - 3*x - 3*E^10*x + E^5*(3 + 2*x^2))*Log[x] + 2*(3 + 3*E^10 - 6*E^5*x + 2*x^2)*Log[x]^2 +
4*(E^5 - x)*Log[x]^3 + Log[x]^4]), x] + 8*E^5*(1 + E^5)*Defer[Int][x/((-10*(1 + (E^10*(6 + E^10))/10) + 12*E^5
*(1 + E^10/3)*x - 4*E^10*x^2 - 12*E^5*(1 + E^10/3)*Log[x] + 12*(1 + E^10)*x*Log[x] - 8*E^5*x^2*Log[x] - 6*(1 +
E^10)*Log[x]^2 + 12*E^5*x*Log[x]^2 - 4*x^2*Log[x]^2 - 4*E^5*Log[x]^3 + 4*x*Log[x]^3 - Log[x]^4)*Log[10*(1 + E
^20/10) - 4*E^5*(3 + E^10)*x + E^10*(6 + 4*x^2) + 4*(E^15 - 3*x - 3*E^10*x + E^5*(3 + 2*x^2))*Log[x] + 2*(3 +
3*E^10 - 6*E^5*x + 2*x^2)*Log[x]^2 + 4*(E^5 - x)*Log[x]^3 + Log[x]^4]), x] + 12*(1 + E^10)*Defer[Int][Log[x]/(
x*(-10*(1 + (E^10*(6 + E^10))/10) + 12*E^5*(1 + E^10/3)*x - 4*E^10*x^2 - 12*E^5*(1 + E^10/3)*Log[x] + 12*(1 +
E^10)*x*Log[x] - 8*E^5*x^2*Log[x] - 6*(1 + E^10)*Log[x]^2 + 12*E^5*x*Log[x]^2 - 4*x^2*Log[x]^2 - 4*E^5*Log[x]^
3 + 4*x*Log[x]^3 - Log[x]^4)*Log[10*(1 + E^20/10) - 4*E^5*(3 + E^10)*x + E^10*(6 + 4*x^2) + 4*(E^15 - 3*x - 3*
E^10*x + E^5*(3 + 2*x^2))*Log[x] + 2*(3 + 3*E^10 - 6*E^5*x + 2*x^2)*Log[x]^2 + 4*(E^5 - x)*Log[x]^3 + Log[x]^4
]), x] + 8*(1 + 2*E^5)*Defer[Int][(x*Log[x])/((-10*(1 + (E^10*(6 + E^10))/10) + 12*E^5*(1 + E^10/3)*x - 4*E^10
*x^2 - 12*E^5*(1 + E^10/3)*Log[x] + 12*(1 + E^10)*x*Log[x] - 8*E^5*x^2*Log[x] - 6*(1 + E^10)*Log[x]^2 + 12*E^5
*x*Log[x]^2 - 4*x^2*Log[x]^2 - 4*E^5*Log[x]^3 + 4*x*Log[x]^3 - Log[x]^4)*Log[10*(1 + E^20/10) - 4*E^5*(3 + E^1
0)*x + E^10*(6 + 4*x^2) + 4*(E^15 - 3*x - 3*E^10*x + E^5*(3 + 2*x^2))*Log[x] + 2*(3 + 3*E^10 - 6*E^5*x + 2*x^2
)*Log[x]^2 + 4*(E^5 - x)*Log[x]^3 + Log[x]^4]), x] + 12*E^5*Defer[Int][Log[x]^2/(x*(-10*(1 + (E^10*(6 + E^10))
/10) + 12*E^5*(1 + E^10/3)*x - 4*E^10*x^2 - 12*E^5*(1 + E^10/3)*Log[x] + 12*(1 + E^10)*x*Log[x] - 8*E^5*x^2*Lo
g[x] - 6*(1 + E^10)*Log[x]^2 + 12*E^5*x*Log[x]^2 - 4*x^2*Log[x]^2 - 4*E^5*Log[x]^3 + 4*x*Log[x]^3 - Log[x]^4)*
Log[10*(1 + E^20/10) - 4*E^5*(3 + E^10)*x + E^10*(6 + 4*x^2) + 4*(E^15 - 3*x - 3*E^10*x + E^5*(3 + 2*x^2))*Log
[x] + 2*(3 + 3*E^10 - 6*E^5*x + 2*x^2)*Log[x]^2 + 4*(E^5 - x)*Log[x]^3 + Log[x]^4]), x] + 8*Defer[Int][(x*Log[
x]^2)/((-10*(1 + (E^10*(6 + E^10))/10) + 12*E^5*(1 + E^10/3)*x - 4*E^10*x^2 - 12*E^5*(1 + E^10/3)*Log[x] + 12*
(1 + E^10)*x*Log[x] - 8*E^5*x^2*Log[x] - 6*(1 + E^10)*Log[x]^2 + 12*E^5*x*Log[x]^2 - 4*x^2*Log[x]^2 - 4*E^5*Lo
g[x]^3 + 4*x*Log[x]^3 - Log[x]^4)*Log[10*(1 + E^20/10) - 4*E^5*(3 + E^10)*x + E^10*(6 + 4*x^2) + 4*(E^15 - 3*x
- 3*E^10*x + E^5*(3 + 2*x^2))*Log[x] + 2*(3 + 3*E^10 - 6*E^5*x + 2*x^2)*Log[x]^2 + 4*(E^5 - x)*Log[x]^3 + Log
[x]^4]), x] + 4*Defer[Int][Log[x]^3/(x*(-10*(1 + (E^10*(6 + E^10))/10) + 12*E^5*(1 + E^10/3)*x - 4*E^10*x^2 -
12*E^5*(1 + E^10/3)*Log[x] + 12*(1 + E^10)*x*Log[x] - 8*E^5*x^2*Log[x] - 6*(1 + E^10)*Log[x]^2 + 12*E^5*x*Log[
x]^2 - 4*x^2*Log[x]^2 - 4*E^5*Log[x]^3 + 4*x*Log[x]^3 - Log[x]^4)*Log[10*(1 + E^20/10) - 4*E^5*(3 + E^10)*x +
E^10*(6 + 4*x^2) + 4*(E^15 - 3*x - 3*E^10*x + E^5*(3 + 2*x^2))*Log[x] + 2*(3 + 3*E^10 - 6*E^5*x + 2*x^2)*Log[x
]^2 + 4*(E^5 - x)*Log[x]^3 + Log[x]^4]), x] + 4*(3 + 3*E^5 + 3*E^10 + E^15)*Defer[Int][1/((10*(1 + (E^10*(6 +
E^10))/10) - 12*E^5*(1 + E^10/3)*x + 4*E^10*x^2 + 12*E^5*(1 + E^10/3)*Log[x] - 12*(1 + E^10)*x*Log[x] + 8*E^5*
x^2*Log[x] + 6*(1 + E^10)*Log[x]^2 - 12*E^5*x*Log[x]^2 + 4*x^2*Log[x]^2 + 4*E^5*Log[x]^3 - 4*x*Log[x]^3 + Log[
x]^4)*Log[10*(1 + E^20/10) - 4*E^5*(3 + E^10)*x + E^10*(6 + 4*x^2) + 4*(E^15 - 3*x - 3*E^10*x + E^5*(3 + 2*x^2
))*Log[x] + 2*(3 + 3*E^10 - 6*E^5*x + 2*x^2)*Log[x]^2 + 4*(E^5 - x)*Log[x]^3 + Log[x]^4]), x] + 12*(1 + E^5)^2
*Defer[Int][Log[x]/((10*(1 + (E^10*(6 + E^10))/10) - 12*E^5*(1 + E^10/3)*x + 4*E^10*x^2 + 12*E^5*(1 + E^10/3)*
Log[x] - 12*(1 + E^10)*x*Log[x] + 8*E^5*x^2*Log[x] + 6*(1 + E^10)*Log[x]^2 - 12*E^5*x*Log[x]^2 + 4*x^2*Log[x]^
2 + 4*E^5*Log[x]^3 - 4*x*Log[x]^3 + Log[x]^4)*Log[10*(1 + E^20/10) - 4*E^5*(3 + E^10)*x + E^10*(6 + 4*x^2) + 4
*(E^15 - 3*x - 3*E^10*x + E^5*(3 + 2*x^2))*Log[x] + 2*(3 + 3*E^10 - 6*E^5*x + 2*x^2)*Log[x]^2 + 4*(E^5 - x)*Lo
g[x]^3 + Log[x]^4]), x] + 12*(1 + E^5)*Defer[Int][Log[x]^2/((10*(1 + (E^10*(6 + E^10))/10) - 12*E^5*(1 + E^10/
3)*x + 4*E^10*x^2 + 12*E^5*(1 + E^10/3)*Log[x] - 12*(1 + E^10)*x*Log[x] + 8*E^5*x^2*Log[x] + 6*(1 + E^10)*Log[
x]^2 - 12*E^5*x*Log[x]^2 + 4*x^2*Log[x]^2 + 4*E^5*Log[x]^3 - 4*x*Log[x]^3 + Log[x]^4)*Log[10*(1 + E^20/10) - 4
*E^5*(3 + E^10)*x + E^10*(6 + 4*x^2) + 4*(E^15 - 3*x - 3*E^10*x + E^5*(3 + 2*x^2))*Log[x] + 2*(3 + 3*E^10 - 6*
E^5*x + 2*x^2)*Log[x]^2 + 4*(E^5 - x)*Log[x]^3 + Log[x]^4]), x] + 4*Defer[Int][Log[x]^3/((10*(1 + (E^10*(6 + E
^10))/10) - 12*E^5*(1 + E^10/3)*x + 4*E^10*x^2 + 12*E^5*(1 + E^10/3)*Log[x] - 12*(1 + E^10)*x*Log[x] + 8*E^5*x
^2*Log[x] + 6*(1 + E^10)*Log[x]^2 - 12*E^5*x*Log[x]^2 + 4*x^2*Log[x]^2 + 4*E^5*Log[x]^3 - 4*x*Log[x]^3 + Log[x
]^4)*Log[10*(1 + E^20/10) - 4*E^5*(3 + E^10)*x + E^10*(6 + 4*x^2) + 4*(E^15 - 3*x - 3*E^10*x + E^5*(3 + 2*x^2)
)*Log[x] + 2*(3 + 3*E^10 - 6*E^5*x + 2*x^2)*Log[x]^2 + 4*(E^5 - x)*Log[x]^3 + Log[x]^4]), x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (\left (10+e^{20}\right ) x-12 e^5 x^2-4 e^{15} x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx\\ &=\int \frac {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (\left (10+e^{20}\right ) x+\left (-12 e^5-4 e^{15}\right ) x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx\\ &=\int \frac {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (\left (10+e^{20}\right ) x+\left (-12 e^5-4 e^{15}\right ) x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10 \left (1+\frac {e^{20}}{10}\right )-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 0.13, size = 101, normalized size = 3.16 \begin {gather*} -\log \left (\log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+4 \left (e^{15}-3 x-3 e^{10} x+e^5 \left (3+2 x^2\right )\right ) \log (x)+2 \left (3+3 e^{10}-6 e^5 x+2 x^2\right ) \log ^2(x)+4 \left (e^5-x\right ) \log ^3(x)+\log ^4(x)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(12*x + E^15*(-4 + 4*x) + E^5*(-12 + 12*x - 8*x^2) + E^10*(12*x - 8*x^2) + (-12 + 12*x - 8*x^2 + E^1
0*(-12 + 12*x) + E^5*(24*x - 16*x^2))*Log[x] + (12*x - 8*x^2 + E^5*(-12 + 12*x))*Log[x]^2 + (-4 + 4*x)*Log[x]^
3)/((10*x + E^20*x - 12*E^5*x^2 - 4*E^15*x^2 + E^10*(6*x + 4*x^3) + (4*E^15*x - 12*x^2 - 12*E^10*x^2 + E^5*(12
*x + 8*x^3))*Log[x] + (6*x + 6*E^10*x - 12*E^5*x^2 + 4*x^3)*Log[x]^2 + (4*E^5*x - 4*x^2)*Log[x]^3 + x*Log[x]^4
)*Log[10 + E^20 - 12*E^5*x - 4*E^15*x + E^10*(6 + 4*x^2) + (4*E^15 - 12*x - 12*E^10*x + E^5*(12 + 8*x^2))*Log[
x] + (6 + 6*E^10 - 12*E^5*x + 4*x^2)*Log[x]^2 + (4*E^5 - 4*x)*Log[x]^3 + Log[x]^4]),x]
[Out]
-Log[Log[10 + E^20 - 12*E^5*x - 4*E^15*x + E^10*(6 + 4*x^2) + 4*(E^15 - 3*x - 3*E^10*x + E^5*(3 + 2*x^2))*Log[
x] + 2*(3 + 3*E^10 - 6*E^5*x + 2*x^2)*Log[x]^2 + 4*(E^5 - x)*Log[x]^3 + Log[x]^4]]
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fricas [B] time = 0.62, size = 95, normalized size = 2.97 \begin {gather*} -\log \left (\log \left (-4 \, {\left (x - e^{5}\right )} \log \relax (x)^{3} + \log \relax (x)^{4} + 2 \, {\left (2 \, x^{2} - 6 \, x e^{5} + 3 \, e^{10} + 3\right )} \log \relax (x)^{2} - 4 \, x e^{15} + 2 \, {\left (2 \, x^{2} + 3\right )} e^{10} - 12 \, x e^{5} - 4 \, {\left (3 \, x e^{10} - {\left (2 \, x^{2} + 3\right )} e^{5} + 3 \, x - e^{15}\right )} \log \relax (x) + e^{20} + 10\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*x-4)*log(x)^3+((12*x-12)*exp(5)-8*x^2+12*x)*log(x)^2+((12*x-12)*exp(5)^2+(-16*x^2+24*x)*exp(5)-8
*x^2+12*x-12)*log(x)+(4*x-4)*exp(5)^3+(-8*x^2+12*x)*exp(5)^2+(-8*x^2+12*x-12)*exp(5)+12*x)/(x*log(x)^4+(4*x*ex
p(5)-4*x^2)*log(x)^3+(6*x*exp(5)^2-12*x^2*exp(5)+4*x^3+6*x)*log(x)^2+(4*x*exp(5)^3-12*x^2*exp(5)^2+(8*x^3+12*x
)*exp(5)-12*x^2)*log(x)+x*exp(5)^4-4*x^2*exp(5)^3+(4*x^3+6*x)*exp(5)^2-12*x^2*exp(5)+10*x)/log(log(x)^4+(4*exp
(5)-4*x)*log(x)^3+(6*exp(5)^2-12*x*exp(5)+4*x^2+6)*log(x)^2+(4*exp(5)^3-12*x*exp(5)^2+(8*x^2+12)*exp(5)-12*x)*
log(x)+exp(5)^4-4*x*exp(5)^3+(4*x^2+6)*exp(5)^2-12*x*exp(5)+10),x, algorithm="fricas")
[Out]
-log(log(-4*(x - e^5)*log(x)^3 + log(x)^4 + 2*(2*x^2 - 6*x*e^5 + 3*e^10 + 3)*log(x)^2 - 4*x*e^15 + 2*(2*x^2 +
3)*e^10 - 12*x*e^5 - 4*(3*x*e^10 - (2*x^2 + 3)*e^5 + 3*x - e^15)*log(x) + e^20 + 10))
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giac [B] time = 3.59, size = 113, normalized size = 3.53 \begin {gather*} -\log \left (\log \left (8 \, x^{2} e^{5} \log \relax (x) + 4 \, x^{2} \log \relax (x)^{2} - 12 \, x e^{5} \log \relax (x)^{2} - 4 \, x \log \relax (x)^{3} + 4 \, e^{5} \log \relax (x)^{3} + \log \relax (x)^{4} + 4 \, x^{2} e^{10} - 12 \, x e^{10} \log \relax (x) + 6 \, e^{10} \log \relax (x)^{2} - 4 \, x e^{15} - 12 \, x e^{5} - 12 \, x \log \relax (x) + 4 \, e^{15} \log \relax (x) + 12 \, e^{5} \log \relax (x) + 6 \, \log \relax (x)^{2} + e^{20} + 6 \, e^{10} + 10\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*x-4)*log(x)^3+((12*x-12)*exp(5)-8*x^2+12*x)*log(x)^2+((12*x-12)*exp(5)^2+(-16*x^2+24*x)*exp(5)-8
*x^2+12*x-12)*log(x)+(4*x-4)*exp(5)^3+(-8*x^2+12*x)*exp(5)^2+(-8*x^2+12*x-12)*exp(5)+12*x)/(x*log(x)^4+(4*x*ex
p(5)-4*x^2)*log(x)^3+(6*x*exp(5)^2-12*x^2*exp(5)+4*x^3+6*x)*log(x)^2+(4*x*exp(5)^3-12*x^2*exp(5)^2+(8*x^3+12*x
)*exp(5)-12*x^2)*log(x)+x*exp(5)^4-4*x^2*exp(5)^3+(4*x^3+6*x)*exp(5)^2-12*x^2*exp(5)+10*x)/log(log(x)^4+(4*exp
(5)-4*x)*log(x)^3+(6*exp(5)^2-12*x*exp(5)+4*x^2+6)*log(x)^2+(4*exp(5)^3-12*x*exp(5)^2+(8*x^2+12)*exp(5)-12*x)*
log(x)+exp(5)^4-4*x*exp(5)^3+(4*x^2+6)*exp(5)^2-12*x*exp(5)+10),x, algorithm="giac")
[Out]
-log(log(8*x^2*e^5*log(x) + 4*x^2*log(x)^2 - 12*x*e^5*log(x)^2 - 4*x*log(x)^3 + 4*e^5*log(x)^3 + log(x)^4 + 4*
x^2*e^10 - 12*x*e^10*log(x) + 6*e^10*log(x)^2 - 4*x*e^15 - 12*x*e^5 - 12*x*log(x) + 4*e^15*log(x) + 12*e^5*log
(x) + 6*log(x)^2 + e^20 + 6*e^10 + 10))
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maple [B] time = 0.06, size = 93, normalized size = 2.91
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\(-\ln \left (\ln \left (\ln \relax (x )^{4}+\left (4 \,{\mathrm e}^{5}-4 x \right ) \ln \relax (x )^{3}+\left (6 \,{\mathrm e}^{10}-12 x \,{\mathrm e}^{5}+4 x^{2}+6\right ) \ln \relax (x )^{2}+\left (4 \,{\mathrm e}^{15}-12 x \,{\mathrm e}^{10}+\left (8 x^{2}+12\right ) {\mathrm e}^{5}-12 x \right ) \ln \relax (x )+{\mathrm e}^{20}-4 x \,{\mathrm e}^{15}+\left (4 x^{2}+6\right ) {\mathrm e}^{10}-12 x \,{\mathrm e}^{5}+10\right )\right )\) |
\(93\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((4*x-4)*ln(x)^3+((12*x-12)*exp(5)-8*x^2+12*x)*ln(x)^2+((12*x-12)*exp(5)^2+(-16*x^2+24*x)*exp(5)-8*x^2+12*
x-12)*ln(x)+(4*x-4)*exp(5)^3+(-8*x^2+12*x)*exp(5)^2+(-8*x^2+12*x-12)*exp(5)+12*x)/(x*ln(x)^4+(4*x*exp(5)-4*x^2
)*ln(x)^3+(6*x*exp(5)^2-12*x^2*exp(5)+4*x^3+6*x)*ln(x)^2+(4*x*exp(5)^3-12*x^2*exp(5)^2+(8*x^3+12*x)*exp(5)-12*
x^2)*ln(x)+x*exp(5)^4-4*x^2*exp(5)^3+(4*x^3+6*x)*exp(5)^2-12*x^2*exp(5)+10*x)/ln(ln(x)^4+(4*exp(5)-4*x)*ln(x)^
3+(6*exp(5)^2-12*x*exp(5)+4*x^2+6)*ln(x)^2+(4*exp(5)^3-12*x*exp(5)^2+(8*x^2+12)*exp(5)-12*x)*ln(x)+exp(5)^4-4*
x*exp(5)^3+(4*x^2+6)*exp(5)^2-12*x*exp(5)+10),x,method=_RETURNVERBOSE)
[Out]
-ln(ln(ln(x)^4+(4*exp(5)-4*x)*ln(x)^3+(6*exp(10)-12*x*exp(5)+4*x^2+6)*ln(x)^2+(4*exp(15)-12*x*exp(10)+(8*x^2+1
2)*exp(5)-12*x)*ln(x)+exp(20)-4*x*exp(15)+(4*x^2+6)*exp(10)-12*x*exp(5)+10))
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maxima [B] time = 1.10, size = 92, normalized size = 2.88 \begin {gather*} -\log \left (\log \left (-4 \, {\left (x - e^{5}\right )} \log \relax (x)^{3} + \log \relax (x)^{4} + 4 \, x^{2} e^{10} + 2 \, {\left (2 \, x^{2} - 6 \, x e^{5} + 3 \, e^{10} + 3\right )} \log \relax (x)^{2} - 4 \, x {\left (e^{15} + 3 \, e^{5}\right )} + 4 \, {\left (2 \, x^{2} e^{5} - 3 \, x {\left (e^{10} + 1\right )} + e^{15} + 3 \, e^{5}\right )} \log \relax (x) + e^{20} + 6 \, e^{10} + 10\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*x-4)*log(x)^3+((12*x-12)*exp(5)-8*x^2+12*x)*log(x)^2+((12*x-12)*exp(5)^2+(-16*x^2+24*x)*exp(5)-8
*x^2+12*x-12)*log(x)+(4*x-4)*exp(5)^3+(-8*x^2+12*x)*exp(5)^2+(-8*x^2+12*x-12)*exp(5)+12*x)/(x*log(x)^4+(4*x*ex
p(5)-4*x^2)*log(x)^3+(6*x*exp(5)^2-12*x^2*exp(5)+4*x^3+6*x)*log(x)^2+(4*x*exp(5)^3-12*x^2*exp(5)^2+(8*x^3+12*x
)*exp(5)-12*x^2)*log(x)+x*exp(5)^4-4*x^2*exp(5)^3+(4*x^3+6*x)*exp(5)^2-12*x^2*exp(5)+10*x)/log(log(x)^4+(4*exp
(5)-4*x)*log(x)^3+(6*exp(5)^2-12*x*exp(5)+4*x^2+6)*log(x)^2+(4*exp(5)^3-12*x*exp(5)^2+(8*x^2+12)*exp(5)-12*x)*
log(x)+exp(5)^4-4*x*exp(5)^3+(4*x^2+6)*exp(5)^2-12*x*exp(5)+10),x, algorithm="maxima")
[Out]
-log(log(-4*(x - e^5)*log(x)^3 + log(x)^4 + 4*x^2*e^10 + 2*(2*x^2 - 6*x*e^5 + 3*e^10 + 3)*log(x)^2 - 4*x*(e^15
+ 3*e^5) + 4*(2*x^2*e^5 - 3*x*(e^10 + 1) + e^15 + 3*e^5)*log(x) + e^20 + 6*e^10 + 10))
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mupad [B] time = 3.63, size = 95, normalized size = 2.97 \begin {gather*} -\ln \left (\ln \left ({\ln \relax (x)}^4+\left (4\,{\mathrm {e}}^5-4\,x\right )\,{\ln \relax (x)}^3+\left (4\,x^2-12\,{\mathrm {e}}^5\,x+6\,{\mathrm {e}}^{10}+6\right )\,{\ln \relax (x)}^2+\left (4\,{\mathrm {e}}^{15}-12\,x-12\,x\,{\mathrm {e}}^{10}+{\mathrm {e}}^5\,\left (8\,x^2+12\right )\right )\,\ln \relax (x)+{\mathrm {e}}^{20}-12\,x\,{\mathrm {e}}^5-4\,x\,{\mathrm {e}}^{15}+{\mathrm {e}}^{10}\,\left (4\,x^2+6\right )+10\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((12*x + log(x)^2*(12*x - 8*x^2 + exp(5)*(12*x - 12)) + exp(10)*(12*x - 8*x^2) - exp(5)*(8*x^2 - 12*x + 12)
+ log(x)^3*(4*x - 4) + log(x)*(12*x + exp(5)*(24*x - 16*x^2) - 8*x^2 + exp(10)*(12*x - 12) - 12) + exp(15)*(4
*x - 4))/(log(exp(20) + log(x)^2*(6*exp(10) - 12*x*exp(5) + 4*x^2 + 6) - 12*x*exp(5) - 4*x*exp(15) + log(x)^4
+ exp(10)*(4*x^2 + 6) - log(x)^3*(4*x - 4*exp(5)) - log(x)*(12*x - 4*exp(15) + 12*x*exp(10) - exp(5)*(8*x^2 +
12)) + 10)*(10*x + x*log(x)^4 + exp(10)*(6*x + 4*x^3) + x*exp(20) + log(x)^3*(4*x*exp(5) - 4*x^2) - 12*x^2*exp
(5) - 4*x^2*exp(15) + log(x)*(exp(5)*(12*x + 8*x^3) + 4*x*exp(15) - 12*x^2*exp(10) - 12*x^2) + log(x)^2*(6*x +
6*x*exp(10) - 12*x^2*exp(5) + 4*x^3))),x)
[Out]
-log(log(exp(20) + log(x)^2*(6*exp(10) - 12*x*exp(5) + 4*x^2 + 6) - 12*x*exp(5) - 4*x*exp(15) + log(x)^4 + exp
(10)*(4*x^2 + 6) - log(x)^3*(4*x - 4*exp(5)) - log(x)*(12*x - 4*exp(15) + 12*x*exp(10) - exp(5)*(8*x^2 + 12))
+ 10))
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sympy [B] time = 12.68, size = 104, normalized size = 3.25 \begin {gather*} - \log {\left (\log {\left (- 4 x e^{15} - 12 x e^{5} + \left (- 4 x + 4 e^{5}\right ) \log {\relax (x )}^{3} + \left (4 x^{2} + 6\right ) e^{10} + \left (4 x^{2} - 12 x e^{5} + 6 + 6 e^{10}\right ) \log {\relax (x )}^{2} + \left (- 12 x e^{10} - 12 x + \left (8 x^{2} + 12\right ) e^{5} + 4 e^{15}\right ) \log {\relax (x )} + \log {\relax (x )}^{4} + 10 + e^{20} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*x-4)*ln(x)**3+((12*x-12)*exp(5)-8*x**2+12*x)*ln(x)**2+((12*x-12)*exp(5)**2+(-16*x**2+24*x)*exp(5
)-8*x**2+12*x-12)*ln(x)+(4*x-4)*exp(5)**3+(-8*x**2+12*x)*exp(5)**2+(-8*x**2+12*x-12)*exp(5)+12*x)/(x*ln(x)**4+
(4*x*exp(5)-4*x**2)*ln(x)**3+(6*x*exp(5)**2-12*x**2*exp(5)+4*x**3+6*x)*ln(x)**2+(4*x*exp(5)**3-12*x**2*exp(5)*
*2+(8*x**3+12*x)*exp(5)-12*x**2)*ln(x)+x*exp(5)**4-4*x**2*exp(5)**3+(4*x**3+6*x)*exp(5)**2-12*x**2*exp(5)+10*x
)/ln(ln(x)**4+(4*exp(5)-4*x)*ln(x)**3+(6*exp(5)**2-12*x*exp(5)+4*x**2+6)*ln(x)**2+(4*exp(5)**3-12*x*exp(5)**2+
(8*x**2+12)*exp(5)-12*x)*ln(x)+exp(5)**4-4*x*exp(5)**3+(4*x**2+6)*exp(5)**2-12*x*exp(5)+10),x)
[Out]
-log(log(-4*x*exp(15) - 12*x*exp(5) + (-4*x + 4*exp(5))*log(x)**3 + (4*x**2 + 6)*exp(10) + (4*x**2 - 12*x*exp(
5) + 6 + 6*exp(10))*log(x)**2 + (-12*x*exp(10) - 12*x + (8*x**2 + 12)*exp(5) + 4*exp(15))*log(x) + log(x)**4 +
10 + exp(20)))
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