3.71.26 \(\int \frac {e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 (-32 x-64 x^3)+(-48 x^2-8 e^8 x^2-32 x^4+e^4 (8 x+32 x^3)) \log (3)+(4 x^2+e^8 x^2-4 e^4 x^3+4 x^4) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3))+e^{\frac {2 (16+128 x^2+16 e^8 x^2+64 x^4+e^4 (-32 x-64 x^3)+(-48 x^2-8 e^8 x^2-32 x^4+e^4 (8 x+32 x^3)) \log (3)+(4 x^2+e^8 x^2-4 e^4 x^3+4 x^4) \log ^2(3))}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} (-64+256 x^4+e^4 (64 x-128 x^3)+(-128 x^4+e^4 (-16 x+64 x^3)) \log (3)+(-8 e^4 x^3+16 x^4) \log ^2(3))+(32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)+e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 (-32 x-64 x^3)+(-48 x^2-8 e^8 x^2-32 x^4+e^4 (8 x+32 x^3)) \log (3)+(4 x^2+e^8 x^2-4 e^4 x^3+4 x^4) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} (-64+256 x^4+e^4 (64 x-128 x^3)+(-128 x^4+e^4 (-16 x+64 x^3)) \log (3)+(-8 e^4 x^3+16 x^4) \log ^2(3))) \log (x)}{144 x^3-72 x^3 \log (3)+9 x^3 \log ^2(3)} \, dx\) [7026]
Optimal. Leaf size=37 \[ \frac {1}{9} \left (e^{4+\left (-e^4+2 x+\frac {4}{x (4-\log (3))}\right )^2}+\log (x)\right )^2 \]
[Out]
1/3*(ln(x)+exp((2*x-exp(4)+4/(-ln(3)+4)/x)^2+4))*(1/3*ln(x)+1/3*exp((2*x-exp(4)+4/(-ln(3)+4)/x)^2+4))
________________________________________________________________________________________
Rubi [F]
time = 79.38, 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 {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}\right ) \left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)\right )+\exp \left (\frac {2 \left (16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)\right )}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}\right ) \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )+\left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)+\exp \left (\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}\right ) \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )\right ) \log (x)}{144 x^3-72 x^3 \log (3)+9 x^3 \log ^2(3)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(E^((16 + 128*x^2 + 16*E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4*(8*x
+ 32*x^3))*Log[3] + (4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2)/(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(3
2*x^2 - 16*x^2*Log[3] + 2*x^2*Log[3]^2) + E^((2*(16 + 128*x^2 + 16*E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (
-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4*(8*x + 32*x^3))*Log[3] + (4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2))/(
16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(-64 + 256*x^4 + E^4*(64*x - 128*x^3) + (-128*x^4 + E^4*(-16*x + 64*x^3
))*Log[3] + (-8*E^4*x^3 + 16*x^4)*Log[3]^2) + (32*x^2 - 16*x^2*Log[3] + 2*x^2*Log[3]^2 + E^((16 + 128*x^2 + 16
*E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4*(8*x + 32*x^3))*Log[3] + (4*x^2
+ E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2)/(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(-64 + 256*x^4 + E^4*(64*x -
128*x^3) + (-128*x^4 + E^4*(-16*x + 64*x^3))*Log[3] + (-8*E^4*x^3 + 16*x^4)*Log[3]^2))*Log[x])/(144*x^3 - 72*
x^3*Log[3] + 9*x^3*Log[3]^2),x]
[Out]
Log[x]^2/9 - (8*Log[x]*Defer[Int][E^(4 + (16 - 32*E^4*x - 4*E^4*x^3*(16 + Log[3]^2) + 4*x^4*(16 + Log[3]^2) +
x^2*(E^8*(16 + Log[3]^2) + 4*(32 + Log[3]^2)))/(x^2*(-4 + Log[3])^2))/3^((8*(-E^4 + (6 + E^8)*x - 4*E^4*x^2 +
4*x^3))/(x*(-4 + Log[3])^2)), x])/9 - (8*Defer[Int][E^(4 + (2*(16 - 32*E^4*x - 4*E^4*x^3*(16 + Log[3]^2) + 4*x
^4*(16 + Log[3]^2) + x^2*(E^8*(16 + Log[3]^2) + 4*(32 + Log[3]^2))))/(x^2*(-4 + Log[3])^2))/3^((16*(-E^4 + (6
+ E^8)*x - 4*E^4*x^2 + 4*x^3))/(x*(-4 + Log[3])^2)), x])/9 - (64*Log[x]*Defer[Int][E^((16 - 32*E^4*x - 4*E^4*x
^3*(16 + Log[3]^2) + 4*x^4*(16 + Log[3]^2) + x^2*(E^8*(16 + Log[3]^2) + 4*(32 + Log[3]^2)))/(x^2*(-4 + Log[3])
^2))/(3^((8*(-E^4 + (6 + E^8)*x - 4*E^4*x^2 + 4*x^3))/(x*(-4 + Log[3])^2))*x^3), x])/(9*(4 - Log[3])^2) - (64*
Defer[Int][E^((2*(16 - 32*E^4*x - 4*E^4*x^3*(16 + Log[3]^2) + 4*x^4*(16 + Log[3]^2) + x^2*(E^8*(16 + Log[3]^2)
+ 4*(32 + Log[3]^2))))/(x^2*(-4 + Log[3])^2))/(3^((16*(-E^4 + (6 + E^8)*x - 4*E^4*x^2 + 4*x^3))/(x*(-4 + Log[
3])^2))*x^3), x])/(9*(4 - Log[3])^2) + (8*(8 - Log[9])*Log[x]*Defer[Int][E^(4 + (16 - 32*E^4*x - 4*E^4*x^3*(16
+ Log[3]^2) + 4*x^4*(16 + Log[3]^2) + x^2*(E^8*(16 + Log[3]^2) + 4*(32 + Log[3]^2)))/(x^2*(-4 + Log[3])^2))/(
3^((8*(-E^4 + (6 + E^8)*x - 4*E^4*x^2 + 4*x^3))/(x*(-4 + Log[3])^2))*x^2), x])/(9*(4 - Log[3])^2) + (16*Defer[
Int][E^(4 + (2*(16 - 32*E^4*x - 4*E^4*x^3*(16 + Log[3]^2) + 4*x^4*(16 + Log[3]^2) + x^2*(E^8*(16 + Log[3]^2) +
4*(32 + Log[3]^2))))/(x^2*(-4 + Log[3])^2))/(3^((16*(-E^4 + (6 + E^8)*x - 4*E^4*x^2 + 4*x^3))/(x*(-4 + Log[3]
)^2))*x^2), x])/(9*(4 - Log[3])) + (2*Defer[Int][E^((16 - 32*E^4*x - 4*E^4*x^3*(16 + Log[3]^2) + 4*x^4*(16 + L
og[3]^2) + x^2*(E^8*(16 + Log[3]^2) + 4*(32 + Log[3]^2)))/(x^2*(-4 + Log[3])^2))/(3^((8*(-E^4 + (6 + E^8)*x -
4*E^4*x^2 + 4*x^3))/(x*(-4 + Log[3])^2))*x), x])/9 + (16*Log[x]*Defer[Int][(E^((16 - 32*E^4*x - 4*E^4*x^3*(16
+ Log[3]^2) + 4*x^4*(16 + Log[3]^2) + x^2*(E^8*(16 + Log[3]^2) + 4*(32 + Log[3]^2)))/(x^2*(-4 + Log[3])^2))*x)
/3^((8*(-E^4 + (6 + E^8)*x - 4*E^4*x^2 + 4*x^3))/(x*(-4 + Log[3])^2)), x])/9 + (8*(8 - Log[9])*Defer[Int][(E^(
(2*(16 - 32*E^4*x - 4*E^4*x^3*(16 + Log[3]^2) + 4*x^4*(16 + Log[3]^2) + x^2*(E^8*(16 + Log[3]^2) + 4*(32 + Log
[3]^2))))/(x^2*(-4 + Log[3])^2))*x)/3^((16*(-E^4 + (6 + E^8)*x - 4*E^4*x^2 + 4*x^3))/(x*(-4 + Log[3])^2)), x])
/(9*(4 - Log[3])) + (8*Defer[Int][Defer[Int][E^(4 + (E^8*x^2*(16 + Log[3]^2) - 4*E^4*x*(8 + x^2*(16 + Log[3]^2
)) + 4*(4 + x^4*(16 + Log[3]^2) + x^2*(32 + Log[3]^2)))/(x^2*(-4 + Log[3])^2))/3^((8*(-E^4 + (6 + E^8)*x - 4*E
^4*x^2 + 4*x^3))/(x*(-4 + Log[3])^2)), x]/x, x])/9 + (64*Defer[Int][Defer[Int][E^((16 - 32*E^4*x - 4*E^4*x^3*(
16 + Log[3]^2) + 4*x^4*(16 + Log[3]^2) + x^2*(E^8*(16 + Log[3]^2) + 4*(32 + Log[3]^2)))/(x^2*(-4 + Log[3])^2))
/(3^((8*(-E^4 + (6 + E^8)*x - 4*E^4*x^2 + 4*x^3))/(x*(-4 + Log[3])^2))*x^3), x]/x, x])/(9*(4 - Log[3])^2) - (1
6*Defer[Int][Defer[Int][E^(4 + (E^8*x^2*(16 + Log[3]^2) - 4*E^4*x*(8 + x^2*(16 + Log[3]^2)) + 4*(4 + x^4*(16 +
Log[3]^2) + x^2*(32 + Log[3]^2)))/(x^2*(-4 + Log[3])^2))/(3^((8*(-E^4 + (6 + E^8)*x - 4*E^4*x^2 + 4*x^3))/(x*
(-4 + Log[3])^2))*x^2), x]/x, x])/(9*(4 - Log[3])) - (16*Defer[Int][Defer[Int][(E^((16 - 32*E^4*x - 4*E^4*x^3*
(16 + Log[3]^2) + 4*x^4*(16 + Log[3]^2) + x^2*(E^8*(16 + Log[3]^2) + 4*(32 + Log[3]^2)))/(x^2*(-4 + Log[3])^2)
)*x)/3^((8*(-E^4 + (6 + E^8)*x - 4*E^4*x^2 + 4*x^3))/(x*(-4 + Log[3])^2)), x]/x, x])/9
Rubi steps
Aborted
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(107\) vs. \(2(37)=74\).
time = 1.40, size = 107, normalized size = 2.89 \begin {gather*} \frac {1}{9} e^{-\frac {8 \left (8+e^8+e^4 x (-4+\log (3))\right )}{-4+\log (3)}} \left (3^{\frac {4+e^8}{-4+\log (3)}} e^{\frac {4 \left (4+x^4 (-4+\log (3))^2+e^4 x (-8+\log (9))\right )}{x^2 (-4+\log (3))^2}}+e^{\frac {4 \left (8+e^8+e^4 x (-4+\log (3))\right )}{-4+\log (3)}} \log (x)\right )^2 \end {gather*}
Warning: Unable to verify antiderivative.
[In]
Integrate[(E^((16 + 128*x^2 + 16*E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4
*(8*x + 32*x^3))*Log[3] + (4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2)/(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^
2))*(32*x^2 - 16*x^2*Log[3] + 2*x^2*Log[3]^2) + E^((2*(16 + 128*x^2 + 16*E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^
3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4*(8*x + 32*x^3))*Log[3] + (4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]
^2))/(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(-64 + 256*x^4 + E^4*(64*x - 128*x^3) + (-128*x^4 + E^4*(-16*x +
64*x^3))*Log[3] + (-8*E^4*x^3 + 16*x^4)*Log[3]^2) + (32*x^2 - 16*x^2*Log[3] + 2*x^2*Log[3]^2 + E^((16 + 128*x^
2 + 16*E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4*(8*x + 32*x^3))*Log[3] +
(4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2)/(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(-64 + 256*x^4 + E^4*(
64*x - 128*x^3) + (-128*x^4 + E^4*(-16*x + 64*x^3))*Log[3] + (-8*E^4*x^3 + 16*x^4)*Log[3]^2))*Log[x])/(144*x^3
- 72*x^3*Log[3] + 9*x^3*Log[3]^2),x]
[Out]
(3^((4 + E^8)/(-4 + Log[3]))*E^((4*(4 + x^4*(-4 + Log[3])^2 + E^4*x*(-8 + Log[9])))/(x^2*(-4 + Log[3])^2)) + E
^((4*(8 + E^8 + E^4*x*(-4 + Log[3])))/(-4 + Log[3]))*Log[x])^2/(9*E^((8*(8 + E^8 + E^4*x*(-4 + Log[3])))/(-4 +
Log[3])))
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(275\) vs.
\(2(64)=128\).
time = 3.48, size = 276, normalized size = 7.46
| | |
| method |
result |
size |
| | |
| risch |
\(\frac {\ln \left (x \right )^{2}}{9}+\frac {2 \,{\mathrm e}^{-\frac {4 \,{\mathrm e}^{4} \ln \left (3\right )^{2} x^{3}-4 x^{4} \ln \left (3\right )^{2}-32 \,{\mathrm e}^{4} \ln \left (3\right ) x^{3}-\ln \left (3\right )^{2} {\mathrm e}^{8} x^{2}+32 x^{4} \ln \left (3\right )+64 x^{3} {\mathrm e}^{4}-4 x^{2} \ln \left (3\right )^{2}+8 \ln \left (3\right ) {\mathrm e}^{8} x^{2}-64 x^{4}-8 \,{\mathrm e}^{4} x \ln \left (3\right )+48 x^{2} \ln \left (3\right )-16 x^{2} {\mathrm e}^{8}+32 x \,{\mathrm e}^{4}-128 x^{2}-16}{x^{2} \left (-4+\ln \left (3\right )\right )^{2}}} \ln \left (x \right )}{9}+\frac {{\mathrm e}^{-\frac {2 \left (4 \,{\mathrm e}^{4} \ln \left (3\right )^{2} x^{3}-4 x^{4} \ln \left (3\right )^{2}-32 \,{\mathrm e}^{4} \ln \left (3\right ) x^{3}-\ln \left (3\right )^{2} {\mathrm e}^{8} x^{2}+32 x^{4} \ln \left (3\right )+64 x^{3} {\mathrm e}^{4}-4 x^{2} \ln \left (3\right )^{2}+8 \ln \left (3\right ) {\mathrm e}^{8} x^{2}-64 x^{4}-8 \,{\mathrm e}^{4} x \ln \left (3\right )+48 x^{2} \ln \left (3\right )-16 x^{2} {\mathrm e}^{8}+32 x \,{\mathrm e}^{4}-128 x^{2}-16\right )}{x^{2} \left (-4+\ln \left (3\right )\right )^{2}}}}{9}\) |
\(258\) |
| default |
\(\frac {\left (2 \ln \left (3\right )-8\right ) {\mathrm e}^{\frac {\left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+\left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+16 x^{2} {\mathrm e}^{8}+\left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+64 x^{4}+128 x^{2}+16}{x^{2} \ln \left (3\right )^{2}-8 x^{2} \ln \left (3\right )+16 x^{2}}} \ln \left (x \right )}{-36+9 \ln \left (3\right )}+\frac {\ln \left (x \right )^{2}}{9}+\frac {{\mathrm e}^{\frac {2 \left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+2 \left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+32 x^{2} {\mathrm e}^{8}+2 \left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+128 x^{4}+256 x^{2}+32}{x^{2} \ln \left (3\right )^{2}-8 x^{2} \ln \left (3\right )+16 x^{2}}}}{9}\) |
\(276\) |
| | |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((((-8*x^3*exp(4)+16*x^4)*ln(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*ln(3)+(-128*x^3+64*x)*exp(4)+256*x^4-64)*
exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*ln(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2)*ln(3)
+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*ln(3)^2-8*x^2*ln(3)+16*x^2))+2*x^2*ln(3)^2-16*x
^2*ln(3)+32*x^2)*ln(x)+((-8*x^3*exp(4)+16*x^4)*ln(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*ln(3)+(-128*x^3+64*x)*ex
p(4)+256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*ln(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*
x^4-48*x^2)*ln(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*ln(3)^2-8*x^2*ln(3)+16*x^2))^2
+(2*x^2*ln(3)^2-16*x^2*ln(3)+32*x^2)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*ln(3)^2+(-8*x^2*exp(4)^2+(32
*x^3+8*x)*exp(4)-32*x^4-48*x^2)*ln(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*ln(3)^2-8*
x^2*ln(3)+16*x^2)))/(9*x^3*ln(3)^2-72*x^3*ln(3)+144*x^3),x,method=_RETURNVERBOSE)
[Out]
1/9*(2*ln(3)-8)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*ln(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x
^4-48*x^2)*ln(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*ln(3)^2-8*x^2*ln(3)+16*x^2))*ln
(x)/(-4+ln(3))+1/9*ln(x)^2+1/9*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*ln(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8
*x)*exp(4)-32*x^4-48*x^2)*ln(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*ln(3)^2-8*x^2*ln
(3)+16*x^2))^2
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 652 vs.
\(2 (31) = 62\).
time = 0.92, size = 652, normalized size = 17.62 \begin {gather*} {\left (2 \cdot 3^{\frac {8 \, e^{8}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16}} 3^{\frac {48}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16}} e^{\left (\frac {4 \, x^{2} \log \left (3\right )^{2}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} - \frac {4 \, x e^{4} \log \left (3\right )^{2}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {32 \, x^{2} \log \left (3\right )}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {32 \, x e^{4} \log \left (3\right )}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {e^{8} \log \left (3\right )^{2}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {64 \, x^{2}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {64 \, x e^{4}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {4 \, \log \left (3\right )^{2}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {16 \, e^{8}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {8 \, e^{4} \log \left (3\right )}{{\left (\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16\right )} x} + \frac {128}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {32 \, e^{4}}{{\left (\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16\right )} x} + \frac {16}{{\left (\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16\right )} x^{2}}\right )} \log \left (x\right ) + 3^{\frac {16 \, e^{8}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {96}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16}} e^{\left (\frac {64 \, x^{2} \log \left (3\right )}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {128 \, x e^{4}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {64 \, e^{4}}{{\left (\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16\right )} x}\right )} \log \left (x\right )^{2} + e^{\left (\frac {8 \, x^{2} \log \left (3\right )^{2}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} - \frac {8 \, x e^{4} \log \left (3\right )^{2}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {64 \, x e^{4} \log \left (3\right )}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {2 \, e^{8} \log \left (3\right )^{2}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {128 \, x^{2}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {8 \, \log \left (3\right )^{2}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {32 \, e^{8}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {16 \, e^{4} \log \left (3\right )}{{\left (\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16\right )} x} + \frac {256}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} + \frac {32}{{\left (\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16\right )} x^{2}}\right )}\right )} 3^{-\frac {16 \, e^{8}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} - \frac {96}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} - 2} e^{\left (-\frac {64 \, x^{2} \log \left (3\right )}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} - \frac {128 \, x e^{4}}{\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16} - \frac {64 \, e^{4}}{{\left (\log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 16\right )} x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((((-8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*log(3)+(-128*x^3+64*x)*exp(4)+256*
x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x
^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log(3)^2-8*x^2*log(3)+16*x^2))+2*x^2*
log(3)^2-16*x^2*log(3)+32*x^2)*log(x)+((-8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*log(3)+(
-128*x^3+64*x)*exp(4)+256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x
^3+8*x)*exp(4)-32*x^4-48*x^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log(3)^2-8*
x^2*log(3)+16*x^2))^2+(2*x^2*log(3)^2-16*x^2*log(3)+32*x^2)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*log(3
)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+12
8*x^2+16)/(x^2*log(3)^2-8*x^2*log(3)+16*x^2)))/(9*x^3*log(3)^2-72*x^3*log(3)+144*x^3),x, algorithm="maxima")
[Out]
(2*3^(8*e^8/(log(3)^2 - 8*log(3) + 16))*3^(48/(log(3)^2 - 8*log(3) + 16))*e^(4*x^2*log(3)^2/(log(3)^2 - 8*log(
3) + 16) - 4*x*e^4*log(3)^2/(log(3)^2 - 8*log(3) + 16) + 32*x^2*log(3)/(log(3)^2 - 8*log(3) + 16) + 32*x*e^4*l
og(3)/(log(3)^2 - 8*log(3) + 16) + e^8*log(3)^2/(log(3)^2 - 8*log(3) + 16) + 64*x^2/(log(3)^2 - 8*log(3) + 16)
+ 64*x*e^4/(log(3)^2 - 8*log(3) + 16) + 4*log(3)^2/(log(3)^2 - 8*log(3) + 16) + 16*e^8/(log(3)^2 - 8*log(3) +
16) + 8*e^4*log(3)/((log(3)^2 - 8*log(3) + 16)*x) + 128/(log(3)^2 - 8*log(3) + 16) + 32*e^4/((log(3)^2 - 8*lo
g(3) + 16)*x) + 16/((log(3)^2 - 8*log(3) + 16)*x^2))*log(x) + 3^(16*e^8/(log(3)^2 - 8*log(3) + 16) + 96/(log(3
)^2 - 8*log(3) + 16))*e^(64*x^2*log(3)/(log(3)^2 - 8*log(3) + 16) + 128*x*e^4/(log(3)^2 - 8*log(3) + 16) + 64*
e^4/((log(3)^2 - 8*log(3) + 16)*x))*log(x)^2 + e^(8*x^2*log(3)^2/(log(3)^2 - 8*log(3) + 16) - 8*x*e^4*log(3)^2
/(log(3)^2 - 8*log(3) + 16) + 64*x*e^4*log(3)/(log(3)^2 - 8*log(3) + 16) + 2*e^8*log(3)^2/(log(3)^2 - 8*log(3)
+ 16) + 128*x^2/(log(3)^2 - 8*log(3) + 16) + 8*log(3)^2/(log(3)^2 - 8*log(3) + 16) + 32*e^8/(log(3)^2 - 8*log
(3) + 16) + 16*e^4*log(3)/((log(3)^2 - 8*log(3) + 16)*x) + 256/(log(3)^2 - 8*log(3) + 16) + 32/((log(3)^2 - 8*
log(3) + 16)*x^2)))*3^(-16*e^8/(log(3)^2 - 8*log(3) + 16) - 96/(log(3)^2 - 8*log(3) + 16) - 2)*e^(-64*x^2*log(
3)/(log(3)^2 - 8*log(3) + 16) - 128*x*e^4/(log(3)^2 - 8*log(3) + 16) - 64*e^4/((log(3)^2 - 8*log(3) + 16)*x))
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 246 vs.
\(2 (31) = 62\).
time = 0.41, size = 246, normalized size = 6.65 \begin {gather*} \frac {2}{9} \, e^{\left (\frac {64 \, x^{4} + 16 \, x^{2} e^{8} + {\left (4 \, x^{4} - 4 \, x^{3} e^{4} + x^{2} e^{8} + 4 \, x^{2}\right )} \log \left (3\right )^{2} + 128 \, x^{2} - 32 \, {\left (2 \, x^{3} + x\right )} e^{4} - 8 \, {\left (4 \, x^{4} + x^{2} e^{8} + 6 \, x^{2} - {\left (4 \, x^{3} + x\right )} e^{4}\right )} \log \left (3\right ) + 16}{x^{2} \log \left (3\right )^{2} - 8 \, x^{2} \log \left (3\right ) + 16 \, x^{2}}\right )} \log \left (x\right ) + \frac {1}{9} \, \log \left (x\right )^{2} + \frac {1}{9} \, e^{\left (\frac {2 \, {\left (64 \, x^{4} + 16 \, x^{2} e^{8} + {\left (4 \, x^{4} - 4 \, x^{3} e^{4} + x^{2} e^{8} + 4 \, x^{2}\right )} \log \left (3\right )^{2} + 128 \, x^{2} - 32 \, {\left (2 \, x^{3} + x\right )} e^{4} - 8 \, {\left (4 \, x^{4} + x^{2} e^{8} + 6 \, x^{2} - {\left (4 \, x^{3} + x\right )} e^{4}\right )} \log \left (3\right ) + 16\right )}}{x^{2} \log \left (3\right )^{2} - 8 \, x^{2} \log \left (3\right ) + 16 \, x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((((-8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*log(3)+(-128*x^3+64*x)*exp(4)+256*
x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x
^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log(3)^2-8*x^2*log(3)+16*x^2))+2*x^2*
log(3)^2-16*x^2*log(3)+32*x^2)*log(x)+((-8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*log(3)+(
-128*x^3+64*x)*exp(4)+256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x
^3+8*x)*exp(4)-32*x^4-48*x^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log(3)^2-8*
x^2*log(3)+16*x^2))^2+(2*x^2*log(3)^2-16*x^2*log(3)+32*x^2)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*log(3
)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+12
8*x^2+16)/(x^2*log(3)^2-8*x^2*log(3)+16*x^2)))/(9*x^3*log(3)^2-72*x^3*log(3)+144*x^3),x, algorithm="fricas")
[Out]
2/9*e^((64*x^4 + 16*x^2*e^8 + (4*x^4 - 4*x^3*e^4 + x^2*e^8 + 4*x^2)*log(3)^2 + 128*x^2 - 32*(2*x^3 + x)*e^4 -
8*(4*x^4 + x^2*e^8 + 6*x^2 - (4*x^3 + x)*e^4)*log(3) + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*log(x) + 1/
9*log(x)^2 + 1/9*e^(2*(64*x^4 + 16*x^2*e^8 + (4*x^4 - 4*x^3*e^4 + x^2*e^8 + 4*x^2)*log(3)^2 + 128*x^2 - 32*(2*
x^3 + x)*e^4 - 8*(4*x^4 + x^2*e^8 + 6*x^2 - (4*x^3 + x)*e^4)*log(3) + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^
2))
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 264 vs.
\(2 (27) = 54\).
time = 1.22, size = 264, normalized size = 7.14 \begin {gather*} \frac {e^{\frac {2 \cdot \left (64 x^{4} + 128 x^{2} + 16 x^{2} e^{8} + \left (- 64 x^{3} - 32 x\right ) e^{4} + \left (- 32 x^{4} - 8 x^{2} e^{8} - 48 x^{2} + \left (32 x^{3} + 8 x\right ) e^{4}\right ) \log {\left (3 \right )} + \left (4 x^{4} - 4 x^{3} e^{4} + 4 x^{2} + x^{2} e^{8}\right ) \log {\left (3 \right )}^{2} + 16\right )}{- 8 x^{2} \log {\left (3 \right )} + x^{2} \log {\left (3 \right )}^{2} + 16 x^{2}}}}{9} + \frac {2 e^{\frac {64 x^{4} + 128 x^{2} + 16 x^{2} e^{8} + \left (- 64 x^{3} - 32 x\right ) e^{4} + \left (- 32 x^{4} - 8 x^{2} e^{8} - 48 x^{2} + \left (32 x^{3} + 8 x\right ) e^{4}\right ) \log {\left (3 \right )} + \left (4 x^{4} - 4 x^{3} e^{4} + 4 x^{2} + x^{2} e^{8}\right ) \log {\left (3 \right )}^{2} + 16}{- 8 x^{2} \log {\left (3 \right )} + x^{2} \log {\left (3 \right )}^{2} + 16 x^{2}}} \log {\left (x \right )}}{9} + \frac {\log {\left (x \right )}^{2}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((((-8*x**3*exp(4)+16*x**4)*ln(3)**2+((64*x**3-16*x)*exp(4)-128*x**4)*ln(3)+(-128*x**3+64*x)*exp(4)+
256*x**4-64)*exp(((x**2*exp(4)**2-4*x**3*exp(4)+4*x**4+4*x**2)*ln(3)**2+(-8*x**2*exp(4)**2+(32*x**3+8*x)*exp(4
)-32*x**4-48*x**2)*ln(3)+16*x**2*exp(4)**2+(-64*x**3-32*x)*exp(4)+64*x**4+128*x**2+16)/(x**2*ln(3)**2-8*x**2*l
n(3)+16*x**2))+2*x**2*ln(3)**2-16*x**2*ln(3)+32*x**2)*ln(x)+((-8*x**3*exp(4)+16*x**4)*ln(3)**2+((64*x**3-16*x)
*exp(4)-128*x**4)*ln(3)+(-128*x**3+64*x)*exp(4)+256*x**4-64)*exp(((x**2*exp(4)**2-4*x**3*exp(4)+4*x**4+4*x**2)
*ln(3)**2+(-8*x**2*exp(4)**2+(32*x**3+8*x)*exp(4)-32*x**4-48*x**2)*ln(3)+16*x**2*exp(4)**2+(-64*x**3-32*x)*exp
(4)+64*x**4+128*x**2+16)/(x**2*ln(3)**2-8*x**2*ln(3)+16*x**2))**2+(2*x**2*ln(3)**2-16*x**2*ln(3)+32*x**2)*exp(
((x**2*exp(4)**2-4*x**3*exp(4)+4*x**4+4*x**2)*ln(3)**2+(-8*x**2*exp(4)**2+(32*x**3+8*x)*exp(4)-32*x**4-48*x**2
)*ln(3)+16*x**2*exp(4)**2+(-64*x**3-32*x)*exp(4)+64*x**4+128*x**2+16)/(x**2*ln(3)**2-8*x**2*ln(3)+16*x**2)))/(
9*x**3*ln(3)**2-72*x**3*ln(3)+144*x**3),x)
[Out]
exp(2*(64*x**4 + 128*x**2 + 16*x**2*exp(8) + (-64*x**3 - 32*x)*exp(4) + (-32*x**4 - 8*x**2*exp(8) - 48*x**2 +
(32*x**3 + 8*x)*exp(4))*log(3) + (4*x**4 - 4*x**3*exp(4) + 4*x**2 + x**2*exp(8))*log(3)**2 + 16)/(-8*x**2*log(
3) + x**2*log(3)**2 + 16*x**2))/9 + 2*exp((64*x**4 + 128*x**2 + 16*x**2*exp(8) + (-64*x**3 - 32*x)*exp(4) + (-
32*x**4 - 8*x**2*exp(8) - 48*x**2 + (32*x**3 + 8*x)*exp(4))*log(3) + (4*x**4 - 4*x**3*exp(4) + 4*x**2 + x**2*e
xp(8))*log(3)**2 + 16)/(-8*x**2*log(3) + x**2*log(3)**2 + 16*x**2))*log(x)/9 + log(x)**2/9
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 282 vs.
\(2 (31) = 62\).
time = 4.70, size = 282, normalized size = 7.62 \begin {gather*} \frac {2}{9} \, e^{\left (\frac {4 \, x^{4} \log \left (3\right )^{2} - 4 \, x^{3} e^{4} \log \left (3\right )^{2} - 32 \, x^{4} \log \left (3\right ) + 32 \, x^{3} e^{4} \log \left (3\right ) + x^{2} e^{8} \log \left (3\right )^{2} + 64 \, x^{4} - 64 \, x^{3} e^{4} - 8 \, x^{2} e^{8} \log \left (3\right ) + 4 \, x^{2} \log \left (3\right )^{2} + 16 \, x^{2} e^{8} - 48 \, x^{2} \log \left (3\right ) + 8 \, x e^{4} \log \left (3\right ) + 128 \, x^{2} - 32 \, x e^{4} + 16}{x^{2} \log \left (3\right )^{2} - 8 \, x^{2} \log \left (3\right ) + 16 \, x^{2}}\right )} \log \left (x\right ) + \frac {1}{9} \, \log \left (x\right )^{2} + \frac {1}{9} \, e^{\left (\frac {2 \, {\left (4 \, x^{4} \log \left (3\right )^{2} - 4 \, x^{3} e^{4} \log \left (3\right )^{2} - 32 \, x^{4} \log \left (3\right ) + 32 \, x^{3} e^{4} \log \left (3\right ) + x^{2} e^{8} \log \left (3\right )^{2} + 64 \, x^{4} - 64 \, x^{3} e^{4} - 8 \, x^{2} e^{8} \log \left (3\right ) + 4 \, x^{2} \log \left (3\right )^{2} + 16 \, x^{2} e^{8} - 48 \, x^{2} \log \left (3\right ) + 8 \, x e^{4} \log \left (3\right ) + 128 \, x^{2} - 32 \, x e^{4} + 16\right )}}{x^{2} \log \left (3\right )^{2} - 8 \, x^{2} \log \left (3\right ) + 16 \, x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((((-8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*log(3)+(-128*x^3+64*x)*exp(4)+256*
x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x
^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log(3)^2-8*x^2*log(3)+16*x^2))+2*x^2*
log(3)^2-16*x^2*log(3)+32*x^2)*log(x)+((-8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*log(3)+(
-128*x^3+64*x)*exp(4)+256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x
^3+8*x)*exp(4)-32*x^4-48*x^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log(3)^2-8*
x^2*log(3)+16*x^2))^2+(2*x^2*log(3)^2-16*x^2*log(3)+32*x^2)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*log(3
)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+12
8*x^2+16)/(x^2*log(3)^2-8*x^2*log(3)+16*x^2)))/(9*x^3*log(3)^2-72*x^3*log(3)+144*x^3),x, algorithm="giac")
[Out]
2/9*e^((4*x^4*log(3)^2 - 4*x^3*e^4*log(3)^2 - 32*x^4*log(3) + 32*x^3*e^4*log(3) + x^2*e^8*log(3)^2 + 64*x^4 -
64*x^3*e^4 - 8*x^2*e^8*log(3) + 4*x^2*log(3)^2 + 16*x^2*e^8 - 48*x^2*log(3) + 8*x*e^4*log(3) + 128*x^2 - 32*x*
e^4 + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*log(x) + 1/9*log(x)^2 + 1/9*e^(2*(4*x^4*log(3)^2 - 4*x^3*e^4
*log(3)^2 - 32*x^4*log(3) + 32*x^3*e^4*log(3) + x^2*e^8*log(3)^2 + 64*x^4 - 64*x^3*e^4 - 8*x^2*e^8*log(3) + 4*
x^2*log(3)^2 + 16*x^2*e^8 - 48*x^2*log(3) + 8*x*e^4*log(3) + 128*x^2 - 32*x*e^4 + 16)/(x^2*log(3)^2 - 8*x^2*lo
g(3) + 16*x^2))
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int -\frac {\ln \left (x\right )\,\left (2\,x^2\,{\ln \left (3\right )}^2-16\,x^2\,\ln \left (3\right )-{\mathrm {e}}^{\frac {{\ln \left (3\right )}^2\,\left (x^2\,{\mathrm {e}}^8-4\,x^3\,{\mathrm {e}}^4+4\,x^2+4\,x^4\right )-{\mathrm {e}}^4\,\left (64\,x^3+32\,x\right )-\ln \left (3\right )\,\left (8\,x^2\,{\mathrm {e}}^8-{\mathrm {e}}^4\,\left (32\,x^3+8\,x\right )+48\,x^2+32\,x^4\right )+16\,x^2\,{\mathrm {e}}^8+128\,x^2+64\,x^4+16}{x^2\,{\ln \left (3\right )}^2-8\,x^2\,\ln \left (3\right )+16\,x^2}}\,\left ({\ln \left (3\right )}^2\,\left (8\,x^3\,{\mathrm {e}}^4-16\,x^4\right )-{\mathrm {e}}^4\,\left (64\,x-128\,x^3\right )+\ln \left (3\right )\,\left ({\mathrm {e}}^4\,\left (16\,x-64\,x^3\right )+128\,x^4\right )-256\,x^4+64\right )+32\,x^2\right )+{\mathrm {e}}^{\frac {{\ln \left (3\right )}^2\,\left (x^2\,{\mathrm {e}}^8-4\,x^3\,{\mathrm {e}}^4+4\,x^2+4\,x^4\right )-{\mathrm {e}}^4\,\left (64\,x^3+32\,x\right )-\ln \left (3\right )\,\left (8\,x^2\,{\mathrm {e}}^8-{\mathrm {e}}^4\,\left (32\,x^3+8\,x\right )+48\,x^2+32\,x^4\right )+16\,x^2\,{\mathrm {e}}^8+128\,x^2+64\,x^4+16}{x^2\,{\ln \left (3\right )}^2-8\,x^2\,\ln \left (3\right )+16\,x^2}}\,\left (2\,x^2\,{\ln \left (3\right )}^2-16\,x^2\,\ln \left (3\right )+32\,x^2\right )-{\mathrm {e}}^{\frac {2\,\left ({\ln \left (3\right )}^2\,\left (x^2\,{\mathrm {e}}^8-4\,x^3\,{\mathrm {e}}^4+4\,x^2+4\,x^4\right )-{\mathrm {e}}^4\,\left (64\,x^3+32\,x\right )-\ln \left (3\right )\,\left (8\,x^2\,{\mathrm {e}}^8-{\mathrm {e}}^4\,\left (32\,x^3+8\,x\right )+48\,x^2+32\,x^4\right )+16\,x^2\,{\mathrm {e}}^8+128\,x^2+64\,x^4+16\right )}{x^2\,{\ln \left (3\right )}^2-8\,x^2\,\ln \left (3\right )+16\,x^2}}\,\left ({\ln \left (3\right )}^2\,\left (8\,x^3\,{\mathrm {e}}^4-16\,x^4\right )-{\mathrm {e}}^4\,\left (64\,x-128\,x^3\right )+\ln \left (3\right )\,\left ({\mathrm {e}}^4\,\left (16\,x-64\,x^3\right )+128\,x^4\right )-256\,x^4+64\right )}{9\,x^3\,{\ln \left (3\right )}^2-72\,x^3\,\ln \left (3\right )+144\,x^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((log(x)*(2*x^2*log(3)^2 - 16*x^2*log(3) - exp((log(3)^2*(x^2*exp(8) - 4*x^3*exp(4) + 4*x^2 + 4*x^4) - exp(
4)*(32*x + 64*x^3) - log(3)*(8*x^2*exp(8) - exp(4)*(8*x + 32*x^3) + 48*x^2 + 32*x^4) + 16*x^2*exp(8) + 128*x^2
+ 64*x^4 + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*(log(3)^2*(8*x^3*exp(4) - 16*x^4) - exp(4)*(64*x - 128
*x^3) + log(3)*(exp(4)*(16*x - 64*x^3) + 128*x^4) - 256*x^4 + 64) + 32*x^2) + exp((log(3)^2*(x^2*exp(8) - 4*x^
3*exp(4) + 4*x^2 + 4*x^4) - exp(4)*(32*x + 64*x^3) - log(3)*(8*x^2*exp(8) - exp(4)*(8*x + 32*x^3) + 48*x^2 + 3
2*x^4) + 16*x^2*exp(8) + 128*x^2 + 64*x^4 + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*(2*x^2*log(3)^2 - 16*x
^2*log(3) + 32*x^2) - exp((2*(log(3)^2*(x^2*exp(8) - 4*x^3*exp(4) + 4*x^2 + 4*x^4) - exp(4)*(32*x + 64*x^3) -
log(3)*(8*x^2*exp(8) - exp(4)*(8*x + 32*x^3) + 48*x^2 + 32*x^4) + 16*x^2*exp(8) + 128*x^2 + 64*x^4 + 16))/(x^2
*log(3)^2 - 8*x^2*log(3) + 16*x^2))*(log(3)^2*(8*x^3*exp(4) - 16*x^4) - exp(4)*(64*x - 128*x^3) + log(3)*(exp(
4)*(16*x - 64*x^3) + 128*x^4) - 256*x^4 + 64))/(9*x^3*log(3)^2 - 72*x^3*log(3) + 144*x^3),x)
[Out]
-int(-(log(x)*(2*x^2*log(3)^2 - 16*x^2*log(3) - exp((log(3)^2*(x^2*exp(8) - 4*x^3*exp(4) + 4*x^2 + 4*x^4) - ex
p(4)*(32*x + 64*x^3) - log(3)*(8*x^2*exp(8) - exp(4)*(8*x + 32*x^3) + 48*x^2 + 32*x^4) + 16*x^2*exp(8) + 128*x
^2 + 64*x^4 + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*(log(3)^2*(8*x^3*exp(4) - 16*x^4) - exp(4)*(64*x - 1
28*x^3) + log(3)*(exp(4)*(16*x - 64*x^3) + 128*x^4) - 256*x^4 + 64) + 32*x^2) + exp((log(3)^2*(x^2*exp(8) - 4*
x^3*exp(4) + 4*x^2 + 4*x^4) - exp(4)*(32*x + 64*x^3) - log(3)*(8*x^2*exp(8) - exp(4)*(8*x + 32*x^3) + 48*x^2 +
32*x^4) + 16*x^2*exp(8) + 128*x^2 + 64*x^4 + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*(2*x^2*log(3)^2 - 16
*x^2*log(3) + 32*x^2) - exp((2*(log(3)^2*(x^2*exp(8) - 4*x^3*exp(4) + 4*x^2 + 4*x^4) - exp(4)*(32*x + 64*x^3)
- log(3)*(8*x^2*exp(8) - exp(4)*(8*x + 32*x^3) + 48*x^2 + 32*x^4) + 16*x^2*exp(8) + 128*x^2 + 64*x^4 + 16))/(x
^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*(log(3)^2*(8*x^3*exp(4) - 16*x^4) - exp(4)*(64*x - 128*x^3) + log(3)*(ex
p(4)*(16*x - 64*x^3) + 128*x^4) - 256*x^4 + 64))/(9*x^3*log(3)^2 - 72*x^3*log(3) + 144*x^3), x)
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