3.27.37 \(\int \frac {e^{\frac {e^{2 x^4} (1-4 x+8 x^3+4 x^4) \log ^2(2)+e^{2 x^4} (-2+8 x-16 x^3-8 x^4) \log (2) \log (x)+e^{2 x^4} (1-4 x+8 x^3+4 x^4) \log ^2(x)}{x^2}} (e^{2 x^4} ((-2+8 x-16 x^3-8 x^4) \log (2)+(-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8) \log ^2(2))+e^{2 x^4} (2-8 x+16 x^3+8 x^4+(4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8) \log (2)) \log (x)+e^{2 x^4} (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8) \log ^2(x))}{x^3} \, dx\)

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

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Rubi [F]  time = 138.43, 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 {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}\right ) \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((E^(2*x^4)*(1 - 4*x + 8*x^3 + 4*x^4)*Log[2]^2 + E^(2*x^4)*(-2 + 8*x - 16*x^3 - 8*x^4)*Log[2]*Log[x] +
E^(2*x^4)*(1 - 4*x + 8*x^3 + 4*x^4)*Log[x]^2)/x^2)*(E^(2*x^4)*((-2 + 8*x - 16*x^3 - 8*x^4)*Log[2] + (-2 + 4*x
+ 8*x^3 + 16*x^4 - 32*x^5 + 64*x^7 + 32*x^8)*Log[2]^2) + E^(2*x^4)*(2 - 8*x + 16*x^3 + 8*x^4 + (4 - 8*x - 16*x
^3 - 32*x^4 + 64*x^5 - 128*x^7 - 64*x^8)*Log[2])*Log[x] + E^(2*x^4)*(-2 + 4*x + 8*x^3 + 16*x^4 - 32*x^5 + 64*x
^7 + 32*x^8)*Log[x]^2))/x^3,x]

[Out]

-8*(2 - Log[2])*Log[2]*Defer[Int][E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2), x] - 2*Log[2]*(
1 + Log[2])*Defer[Int][E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)/x^3, x] + 2*Log[2]*(4 + Log
[4])*Defer[Int][E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)/x^2, x] - 8*Log[2]*(1 - Log[4])*De
fer[Int][E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*x, x] - 32*Log[2]^2*Defer[Int][E^(2*x^4 +
(E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*x^2, x] + 64*Log[2]^2*Defer[Int][E^(2*x^4 + (E^(2*x^4)*(-1 +
2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*x^4, x] + 32*Log[2]^2*Defer[Int][E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*L
og[x/2]^2)/x^2)*x^5, x] + 8*(2 - Log[4])*Defer[Int][E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2
)*Log[x], x] + 2*(1 + Log[4])*Defer[Int][(E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*Log[x])/
x^3, x] - 4*(2 + Log[4])*Defer[Int][(E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*Log[x])/x^2,
x] + 8*(1 - Log[16])*Defer[Int][E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*x*Log[x], x] + 64*
Log[2]*Defer[Int][E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*x^2*Log[x], x] - 128*Log[2]*Defe
r[Int][E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*x^4*Log[x], x] - 64*Log[2]*Defer[Int][E^(2*
x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*x^5*Log[x], x] + 8*Defer[Int][E^(2*x^4 + (E^(2*x^4)*(-1
+ 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*Log[x]^2, x] - 2*Defer[Int][(E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log
[x/2]^2)/x^2)*Log[x]^2)/x^3, x] + 4*Defer[Int][(E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*Lo
g[x]^2)/x^2, x] + 16*Defer[Int][E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*x*Log[x]^2, x] - 3
2*Defer[Int][E^(2*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*x^2*Log[x]^2, x] + 64*Defer[Int][E^(2
*x^4 + (E^(2*x^4)*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*x^4*Log[x]^2, x] + 32*Defer[Int][E^(2*x^4 + (E^(2*x^4)
*(-1 + 2*x + 2*x^2)^2*Log[x/2]^2)/x^2)*x^5*Log[x]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) \left (-\log (2) \left (1-2 x+\log (2)-4 x^4 \log (2)+8 x^5 \log (2)+8 x^6 \log (2)+x^2 (-2+\log (4))\right )+\left (1-2 x-8 x^4 \log (2)+16 x^5 \log (2)+16 x^6 \log (2)+\log (4)+x^2 (-2+\log (16))\right ) \log (x)-\left (1+2 x^2-4 x^4+8 x^5+8 x^6\right ) \log ^2(x)\right )}{x^3} \, dx\\ &=2 \int \frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) \left (-\log (2) \left (1-2 x+\log (2)-4 x^4 \log (2)+8 x^5 \log (2)+8 x^6 \log (2)+x^2 (-2+\log (4))\right )+\left (1-2 x-8 x^4 \log (2)+16 x^5 \log (2)+16 x^6 \log (2)+\log (4)+x^2 (-2+\log (16))\right ) \log (x)-\left (1+2 x^2-4 x^4+8 x^5+8 x^6\right ) \log ^2(x)\right )}{x^3} \, dx\\ &=2 \int \left (\frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) \log (2) \left (-1+2 x+2 x^2 (1-\log (2))-\log (2)+4 x^4 \log (2)-8 x^5 \log (2)-8 x^6 \log (2)\right )}{x^3}+\frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) \left (1-2 x-8 x^4 \log (2)+16 x^5 \log (2)+16 x^6 \log (2)-2 x^2 (1-\log (4))+\log (4)\right ) \log (x)}{x^3}+\frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (-1+2 x+2 x^2\right ) \left (1+2 x^2-4 x^4+8 x^5+8 x^6\right ) \log ^2(x)}{x^3}\right ) \, dx\\ &=2 \int \frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) \left (1-2 x-8 x^4 \log (2)+16 x^5 \log (2)+16 x^6 \log (2)-2 x^2 (1-\log (4))+\log (4)\right ) \log (x)}{x^3} \, dx+2 \int \frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (-1+2 x+2 x^2\right ) \left (1+2 x^2-4 x^4+8 x^5+8 x^6\right ) \log ^2(x)}{x^3} \, dx+(2 \log (2)) \int \frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) \left (-1+2 x+2 x^2 (1-\log (2))-\log (2)+4 x^4 \log (2)-8 x^5 \log (2)-8 x^6 \log (2)\right )}{x^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F]  time = 8.52, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\frac {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}} \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(E^((E^(2*x^4)*(1 - 4*x + 8*x^3 + 4*x^4)*Log[2]^2 + E^(2*x^4)*(-2 + 8*x - 16*x^3 - 8*x^4)*Log[2]*Log
[x] + E^(2*x^4)*(1 - 4*x + 8*x^3 + 4*x^4)*Log[x]^2)/x^2)*(E^(2*x^4)*((-2 + 8*x - 16*x^3 - 8*x^4)*Log[2] + (-2
+ 4*x + 8*x^3 + 16*x^4 - 32*x^5 + 64*x^7 + 32*x^8)*Log[2]^2) + E^(2*x^4)*(2 - 8*x + 16*x^3 + 8*x^4 + (4 - 8*x
- 16*x^3 - 32*x^4 + 64*x^5 - 128*x^7 - 64*x^8)*Log[2])*Log[x] + E^(2*x^4)*(-2 + 4*x + 8*x^3 + 16*x^4 - 32*x^5
+ 64*x^7 + 32*x^8)*Log[x]^2))/x^3,x]

[Out]

Integrate[(E^((E^(2*x^4)*(1 - 4*x + 8*x^3 + 4*x^4)*Log[2]^2 + E^(2*x^4)*(-2 + 8*x - 16*x^3 - 8*x^4)*Log[2]*Log
[x] + E^(2*x^4)*(1 - 4*x + 8*x^3 + 4*x^4)*Log[x]^2)/x^2)*(E^(2*x^4)*((-2 + 8*x - 16*x^3 - 8*x^4)*Log[2] + (-2
+ 4*x + 8*x^3 + 16*x^4 - 32*x^5 + 64*x^7 + 32*x^8)*Log[2]^2) + E^(2*x^4)*(2 - 8*x + 16*x^3 + 8*x^4 + (4 - 8*x
- 16*x^3 - 32*x^4 + 64*x^5 - 128*x^7 - 64*x^8)*Log[2])*Log[x] + E^(2*x^4)*(-2 + 4*x + 8*x^3 + 16*x^4 - 32*x^5
+ 64*x^7 + 32*x^8)*Log[x]^2))/x^3, x]

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fricas [B]  time = 0.71, size = 85, normalized size = 2.74 \begin {gather*} e^{\left (\frac {{\left (4 \, x^{4} + 8 \, x^{3} - 4 \, x + 1\right )} e^{\left (2 \, x^{4}\right )} \log \relax (2)^{2} - 2 \, {\left (4 \, x^{4} + 8 \, x^{3} - 4 \, x + 1\right )} e^{\left (2 \, x^{4}\right )} \log \relax (2) \log \relax (x) + {\left (4 \, x^{4} + 8 \, x^{3} - 4 \, x + 1\right )} e^{\left (2 \, x^{4}\right )} \log \relax (x)^{2}}{x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^8+64*x^7-32*x^5+16*x^4+8*x^3+4*x-2)*exp(x^4)^2*log(x)^2+((-64*x^8-128*x^7+64*x^5-32*x^4-16*x^
3-8*x+4)*log(2)+8*x^4+16*x^3-8*x+2)*exp(x^4)^2*log(x)+((32*x^8+64*x^7-32*x^5+16*x^4+8*x^3+4*x-2)*log(2)^2+(-8*
x^4-16*x^3+8*x-2)*log(2))*exp(x^4)^2)*exp(((4*x^4+8*x^3-4*x+1)*exp(x^4)^2*log(x)^2+(-8*x^4-16*x^3+8*x-2)*log(2
)*exp(x^4)^2*log(x)+(4*x^4+8*x^3-4*x+1)*log(2)^2*exp(x^4)^2)/x^2)/x^3,x, algorithm="fricas")

[Out]

e^(((4*x^4 + 8*x^3 - 4*x + 1)*e^(2*x^4)*log(2)^2 - 2*(4*x^4 + 8*x^3 - 4*x + 1)*e^(2*x^4)*log(2)*log(x) + (4*x^
4 + 8*x^3 - 4*x + 1)*e^(2*x^4)*log(x)^2)/x^2)

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giac [B]  time = 1.75, size = 174, normalized size = 5.61 \begin {gather*} e^{\left (4 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \relax (2)^{2} - 8 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \relax (2) \log \relax (x) + 4 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \relax (x)^{2} + 8 \, x e^{\left (2 \, x^{4}\right )} \log \relax (2)^{2} - 16 \, x e^{\left (2 \, x^{4}\right )} \log \relax (2) \log \relax (x) + 8 \, x e^{\left (2 \, x^{4}\right )} \log \relax (x)^{2} - \frac {4 \, e^{\left (2 \, x^{4}\right )} \log \relax (2)^{2}}{x} + \frac {8 \, e^{\left (2 \, x^{4}\right )} \log \relax (2) \log \relax (x)}{x} - \frac {4 \, e^{\left (2 \, x^{4}\right )} \log \relax (x)^{2}}{x} + \frac {e^{\left (2 \, x^{4}\right )} \log \relax (2)^{2}}{x^{2}} - \frac {2 \, e^{\left (2 \, x^{4}\right )} \log \relax (2) \log \relax (x)}{x^{2}} + \frac {e^{\left (2 \, x^{4}\right )} \log \relax (x)^{2}}{x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^8+64*x^7-32*x^5+16*x^4+8*x^3+4*x-2)*exp(x^4)^2*log(x)^2+((-64*x^8-128*x^7+64*x^5-32*x^4-16*x^
3-8*x+4)*log(2)+8*x^4+16*x^3-8*x+2)*exp(x^4)^2*log(x)+((32*x^8+64*x^7-32*x^5+16*x^4+8*x^3+4*x-2)*log(2)^2+(-8*
x^4-16*x^3+8*x-2)*log(2))*exp(x^4)^2)*exp(((4*x^4+8*x^3-4*x+1)*exp(x^4)^2*log(x)^2+(-8*x^4-16*x^3+8*x-2)*log(2
)*exp(x^4)^2*log(x)+(4*x^4+8*x^3-4*x+1)*log(2)^2*exp(x^4)^2)/x^2)/x^3,x, algorithm="giac")

[Out]

e^(4*x^2*e^(2*x^4)*log(2)^2 - 8*x^2*e^(2*x^4)*log(2)*log(x) + 4*x^2*e^(2*x^4)*log(x)^2 + 8*x*e^(2*x^4)*log(2)^
2 - 16*x*e^(2*x^4)*log(2)*log(x) + 8*x*e^(2*x^4)*log(x)^2 - 4*e^(2*x^4)*log(2)^2/x + 8*e^(2*x^4)*log(2)*log(x)
/x - 4*e^(2*x^4)*log(x)^2/x + e^(2*x^4)*log(2)^2/x^2 - 2*e^(2*x^4)*log(2)*log(x)/x^2 + e^(2*x^4)*log(x)^2/x^2)

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maple [A]  time = 0.07, size = 33, normalized size = 1.06

method	result	size
risch	\({\mathrm e}^{\frac {{\mathrm e}^{2 x^{4}} \left (2 x^{2}+2 x -1\right )^{2} \left (-\ln \relax (x )+\ln \relax (2)\right )^{2}}{x^{2}}}\)	\(33\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((32*x^8+64*x^7-32*x^5+16*x^4+8*x^3+4*x-2)*exp(x^4)^2*ln(x)^2+((-64*x^8-128*x^7+64*x^5-32*x^4-16*x^3-8*x+4
)*ln(2)+8*x^4+16*x^3-8*x+2)*exp(x^4)^2*ln(x)+((32*x^8+64*x^7-32*x^5+16*x^4+8*x^3+4*x-2)*ln(2)^2+(-8*x^4-16*x^3
+8*x-2)*ln(2))*exp(x^4)^2)*exp(((4*x^4+8*x^3-4*x+1)*exp(x^4)^2*ln(x)^2+(-8*x^4-16*x^3+8*x-2)*ln(2)*exp(x^4)^2*
ln(x)+(4*x^4+8*x^3-4*x+1)*ln(2)^2*exp(x^4)^2)/x^2)/x^3,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [B]  time = 2.00, size = 174, normalized size = 5.61 \begin {gather*} e^{\left (4 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \relax (2)^{2} - 8 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \relax (2) \log \relax (x) + 4 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \relax (x)^{2} + 8 \, x e^{\left (2 \, x^{4}\right )} \log \relax (2)^{2} - 16 \, x e^{\left (2 \, x^{4}\right )} \log \relax (2) \log \relax (x) + 8 \, x e^{\left (2 \, x^{4}\right )} \log \relax (x)^{2} - \frac {4 \, e^{\left (2 \, x^{4}\right )} \log \relax (2)^{2}}{x} + \frac {8 \, e^{\left (2 \, x^{4}\right )} \log \relax (2) \log \relax (x)}{x} - \frac {4 \, e^{\left (2 \, x^{4}\right )} \log \relax (x)^{2}}{x} + \frac {e^{\left (2 \, x^{4}\right )} \log \relax (2)^{2}}{x^{2}} - \frac {2 \, e^{\left (2 \, x^{4}\right )} \log \relax (2) \log \relax (x)}{x^{2}} + \frac {e^{\left (2 \, x^{4}\right )} \log \relax (x)^{2}}{x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^8+64*x^7-32*x^5+16*x^4+8*x^3+4*x-2)*exp(x^4)^2*log(x)^2+((-64*x^8-128*x^7+64*x^5-32*x^4-16*x^
3-8*x+4)*log(2)+8*x^4+16*x^3-8*x+2)*exp(x^4)^2*log(x)+((32*x^8+64*x^7-32*x^5+16*x^4+8*x^3+4*x-2)*log(2)^2+(-8*
x^4-16*x^3+8*x-2)*log(2))*exp(x^4)^2)*exp(((4*x^4+8*x^3-4*x+1)*exp(x^4)^2*log(x)^2+(-8*x^4-16*x^3+8*x-2)*log(2
)*exp(x^4)^2*log(x)+(4*x^4+8*x^3-4*x+1)*log(2)^2*exp(x^4)^2)/x^2)/x^3,x, algorithm="maxima")

[Out]

e^(4*x^2*e^(2*x^4)*log(2)^2 - 8*x^2*e^(2*x^4)*log(2)*log(x) + 4*x^2*e^(2*x^4)*log(x)^2 + 8*x*e^(2*x^4)*log(2)^
2 - 16*x*e^(2*x^4)*log(2)*log(x) + 8*x*e^(2*x^4)*log(x)^2 - 4*e^(2*x^4)*log(2)^2/x + 8*e^(2*x^4)*log(2)*log(x)
/x - 4*e^(2*x^4)*log(x)^2/x + e^(2*x^4)*log(2)^2/x^2 - 2*e^(2*x^4)*log(2)*log(x)/x^2 + e^(2*x^4)*log(x)^2/x^2)

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mupad [B]  time = 2.33, size = 155, normalized size = 5.00 \begin {gather*} \frac {{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x^4}\,{\ln \relax (2)}^2}{x^2}}\,{\mathrm {e}}^{-\frac {4\,{\mathrm {e}}^{2\,x^4}\,{\ln \relax (2)}^2}{x}}\,{\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^{2\,x^4}\,{\ln \relax (2)}^2}\,{\mathrm {e}}^{8\,x\,{\mathrm {e}}^{2\,x^4}\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x^4}\,{\ln \relax (x)}^2}{x^2}}\,{\mathrm {e}}^{-\frac {4\,{\mathrm {e}}^{2\,x^4}\,{\ln \relax (x)}^2}{x}}\,{\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^{2\,x^4}\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{8\,x\,{\mathrm {e}}^{2\,x^4}\,{\ln \relax (2)}^2}}{x^{\frac {2\,{\mathrm {e}}^{2\,x^4}\,\ln \relax (2)\,\left (4\,x^4+8\,x^3-4\,x+1\right )}{x^2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((exp(2*x^4)*log(2)^2*(8*x^3 - 4*x + 4*x^4 + 1) + exp(2*x^4)*log(x)^2*(8*x^3 - 4*x + 4*x^4 + 1) - exp(
2*x^4)*log(2)*log(x)*(16*x^3 - 8*x + 8*x^4 + 2))/x^2)*(exp(2*x^4)*log(x)^2*(4*x + 8*x^3 + 16*x^4 - 32*x^5 + 64
*x^7 + 32*x^8 - 2) - exp(2*x^4)*(log(2)*(16*x^3 - 8*x + 8*x^4 + 2) - log(2)^2*(4*x + 8*x^3 + 16*x^4 - 32*x^5 +
64*x^7 + 32*x^8 - 2)) + exp(2*x^4)*log(x)*(16*x^3 - log(2)*(8*x + 16*x^3 + 32*x^4 - 64*x^5 + 128*x^7 + 64*x^8
- 4) - 8*x + 8*x^4 + 2)))/x^3,x)

[Out]

(exp((exp(2*x^4)*log(2)^2)/x^2)*exp(-(4*exp(2*x^4)*log(2)^2)/x)*exp(4*x^2*exp(2*x^4)*log(2)^2)*exp(8*x*exp(2*x
^4)*log(x)^2)*exp((exp(2*x^4)*log(x)^2)/x^2)*exp(-(4*exp(2*x^4)*log(x)^2)/x)*exp(4*x^2*exp(2*x^4)*log(x)^2)*ex
p(8*x*exp(2*x^4)*log(2)^2))/x^((2*exp(2*x^4)*log(2)*(8*x^3 - 4*x + 4*x^4 + 1))/x^2)

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sympy [B]  time = 2.14, size = 87, normalized size = 2.81 \begin {gather*} e^{\frac {\left (- 8 x^{4} - 16 x^{3} + 8 x - 2\right ) e^{2 x^{4}} \log {\relax (2 )} \log {\relax (x )} + \left (4 x^{4} + 8 x^{3} - 4 x + 1\right ) e^{2 x^{4}} \log {\relax (x )}^{2} + \left (4 x^{4} + 8 x^{3} - 4 x + 1\right ) e^{2 x^{4}} \log {\relax (2 )}^{2}}{x^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x**8+64*x**7-32*x**5+16*x**4+8*x**3+4*x-2)*exp(x**4)**2*ln(x)**2+((-64*x**8-128*x**7+64*x**5-32
*x**4-16*x**3-8*x+4)*ln(2)+8*x**4+16*x**3-8*x+2)*exp(x**4)**2*ln(x)+((32*x**8+64*x**7-32*x**5+16*x**4+8*x**3+4
*x-2)*ln(2)**2+(-8*x**4-16*x**3+8*x-2)*ln(2))*exp(x**4)**2)*exp(((4*x**4+8*x**3-4*x+1)*exp(x**4)**2*ln(x)**2+(
-8*x**4-16*x**3+8*x-2)*ln(2)*exp(x**4)**2*ln(x)+(4*x**4+8*x**3-4*x+1)*ln(2)**2*exp(x**4)**2)/x**2)/x**3,x)

[Out]

exp(((-8*x**4 - 16*x**3 + 8*x - 2)*exp(2*x**4)*log(2)*log(x) + (4*x**4 + 8*x**3 - 4*x + 1)*exp(2*x**4)*log(x)*
*2 + (4*x**4 + 8*x**3 - 4*x + 1)*exp(2*x**4)*log(2)**2)/x**2)

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