3.56.29 \(\int \frac {-16 e^{3+x^2}+e^{x^2} (-2 e^6+16 e^3 x^2) \log (x^2)+(-4 e^3 x+e^6 (1+x)) \log ^2(x^2)+(16 e^{x^2}+e^{x^2} (4 e^3-16 x^2) \log (x^2)+(e^3 (-2-2 x)+4 x) \log ^2(x^2)) \log (\frac {4 e^{2 x^2}+e^{x^2} (-4-4 x) \log (x^2)+(1+2 x+x^2) \log ^2(x^2)}{\log ^2(x^2)})+(-2 e^{x^2} \log (x^2)+(1+x) \log ^2(x^2)) \log ^2(\frac {4 e^{2 x^2}+e^{x^2} (-4-4 x) \log (x^2)+(1+2 x+x^2) \log ^2(x^2)}{\log ^2(x^2)})}{-2 e^{x^2} \log (x^2)+(1+x) \log ^2(x^2)} \, dx\)

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

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Rubi [F]  time = 10.22, 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 {-16 e^{3+x^2}+e^{x^2} \left (-2 e^6+16 e^3 x^2\right ) \log \left (x^2\right )+\left (-4 e^3 x+e^6 (1+x)\right ) \log ^2\left (x^2\right )+\left (16 e^{x^2}+e^{x^2} \left (4 e^3-16 x^2\right ) \log \left (x^2\right )+\left (e^3 (-2-2 x)+4 x\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {4 e^{2 x^2}+e^{x^2} (-4-4 x) \log \left (x^2\right )+\left (1+2 x+x^2\right ) \log ^2\left (x^2\right )}{\log ^2\left (x^2\right )}\right )+\left (-2 e^{x^2} \log \left (x^2\right )+(1+x) \log ^2\left (x^2\right )\right ) \log ^2\left (\frac {4 e^{2 x^2}+e^{x^2} (-4-4 x) \log \left (x^2\right )+\left (1+2 x+x^2\right ) \log ^2\left (x^2\right )}{\log ^2\left (x^2\right )}\right )}{-2 e^{x^2} \log \left (x^2\right )+(1+x) \log ^2\left (x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-16*E^(3 + x^2) + E^x^2*(-2*E^6 + 16*E^3*x^2)*Log[x^2] + (-4*E^3*x + E^6*(1 + x))*Log[x^2]^2 + (16*E^x^2
+ E^x^2*(4*E^3 - 16*x^2)*Log[x^2] + (E^3*(-2 - 2*x) + 4*x)*Log[x^2]^2)*Log[(4*E^(2*x^2) + E^x^2*(-4 - 4*x)*Log
[x^2] + (1 + 2*x + x^2)*Log[x^2]^2)/Log[x^2]^2] + (-2*E^x^2*Log[x^2] + (1 + x)*Log[x^2]^2)*Log[(4*E^(2*x^2) +
E^x^2*(-4 - 4*x)*Log[x^2] + (1 + 2*x + x^2)*Log[x^2]^2)/Log[x^2]^2]^2)/(-2*E^x^2*Log[x^2] + (1 + x)*Log[x^2]^2
),x]

[Out]

E^6*x - (32*x^5)/15 + (16*x^3*ExpIntegralEi[(3*Log[x^2])/2])/(3*(x^2)^(3/2)) - 2*E^3*x*Log[(2*E^x^2 - (1 + x)*
Log[x^2])^2/Log[x^2]^2] + (8*x^3*Log[(2*E^x^2 - (1 + x)*Log[x^2])^2/Log[x^2]^2])/3 - (32*Defer[Int][x^2/(-2*E^
x^2 + Log[x^2] + x*Log[x^2]), x])/3 - (32*Defer[Int][x^3/(-2*E^x^2 + Log[x^2] + x*Log[x^2]), x])/3 - (16*Defer
[Int][(x^3*Log[x^2])/(-2*E^x^2 + Log[x^2] + x*Log[x^2]), x])/3 + (32*Defer[Int][(x^4*Log[x^2])/(-2*E^x^2 + Log
[x^2] + x*Log[x^2]), x])/3 + (32*Defer[Int][(x^5*Log[x^2])/(-2*E^x^2 + Log[x^2] + x*Log[x^2]), x])/3 - 8*Defer
[Int][Log[(-2*E^x^2 + (1 + x)*Log[x^2])^2/Log[x^2]^2]/Log[x^2], x] - 8*Defer[Int][Log[(-2*E^x^2 + (1 + x)*Log[
x^2])^2/Log[x^2]^2]/(2*E^x^2 - Log[x^2] - x*Log[x^2]), x] + 8*Defer[Int][(x*Log[(-2*E^x^2 + (1 + x)*Log[x^2])^
2/Log[x^2]^2])/(-2*E^x^2 + Log[x^2] + x*Log[x^2]), x] + 4*Defer[Int][(x*Log[x^2]*Log[(-2*E^x^2 + (1 + x)*Log[x
^2])^2/Log[x^2]^2])/(-2*E^x^2 + Log[x^2] + x*Log[x^2]), x] - 8*Defer[Int][(x^2*Log[x^2]*Log[(-2*E^x^2 + (1 + x
)*Log[x^2])^2/Log[x^2]^2])/(-2*E^x^2 + Log[x^2] + x*Log[x^2]), x] - 8*Defer[Int][(x^3*Log[x^2]*Log[(-2*E^x^2 +
(1 + x)*Log[x^2])^2/Log[x^2]^2])/(-2*E^x^2 + Log[x^2] + x*Log[x^2]), x] + Defer[Int][Log[(-2*E^x^2 + (1 + x)*
Log[x^2])^2/Log[x^2]^2]^2, x]

Rubi steps

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

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Mathematica [F]  time = 1.72, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-16 e^{3+x^2}+e^{x^2} \left (-2 e^6+16 e^3 x^2\right ) \log \left (x^2\right )+\left (-4 e^3 x+e^6 (1+x)\right ) \log ^2\left (x^2\right )+\left (16 e^{x^2}+e^{x^2} \left (4 e^3-16 x^2\right ) \log \left (x^2\right )+\left (e^3 (-2-2 x)+4 x\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {4 e^{2 x^2}+e^{x^2} (-4-4 x) \log \left (x^2\right )+\left (1+2 x+x^2\right ) \log ^2\left (x^2\right )}{\log ^2\left (x^2\right )}\right )+\left (-2 e^{x^2} \log \left (x^2\right )+(1+x) \log ^2\left (x^2\right )\right ) \log ^2\left (\frac {4 e^{2 x^2}+e^{x^2} (-4-4 x) \log \left (x^2\right )+\left (1+2 x+x^2\right ) \log ^2\left (x^2\right )}{\log ^2\left (x^2\right )}\right )}{-2 e^{x^2} \log \left (x^2\right )+(1+x) \log ^2\left (x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-16*E^(3 + x^2) + E^x^2*(-2*E^6 + 16*E^3*x^2)*Log[x^2] + (-4*E^3*x + E^6*(1 + x))*Log[x^2]^2 + (16*
E^x^2 + E^x^2*(4*E^3 - 16*x^2)*Log[x^2] + (E^3*(-2 - 2*x) + 4*x)*Log[x^2]^2)*Log[(4*E^(2*x^2) + E^x^2*(-4 - 4*
x)*Log[x^2] + (1 + 2*x + x^2)*Log[x^2]^2)/Log[x^2]^2] + (-2*E^x^2*Log[x^2] + (1 + x)*Log[x^2]^2)*Log[(4*E^(2*x
^2) + E^x^2*(-4 - 4*x)*Log[x^2] + (1 + 2*x + x^2)*Log[x^2]^2)/Log[x^2]^2]^2)/(-2*E^x^2*Log[x^2] + (1 + x)*Log[
x^2]^2),x]

[Out]

Integrate[(-16*E^(3 + x^2) + E^x^2*(-2*E^6 + 16*E^3*x^2)*Log[x^2] + (-4*E^3*x + E^6*(1 + x))*Log[x^2]^2 + (16*
E^x^2 + E^x^2*(4*E^3 - 16*x^2)*Log[x^2] + (E^3*(-2 - 2*x) + 4*x)*Log[x^2]^2)*Log[(4*E^(2*x^2) + E^x^2*(-4 - 4*
x)*Log[x^2] + (1 + 2*x + x^2)*Log[x^2]^2)/Log[x^2]^2] + (-2*E^x^2*Log[x^2] + (1 + x)*Log[x^2]^2)*Log[(4*E^(2*x
^2) + E^x^2*(-4 - 4*x)*Log[x^2] + (1 + 2*x + x^2)*Log[x^2]^2)/Log[x^2]^2]^2)/(-2*E^x^2*Log[x^2] + (1 + x)*Log[
x^2]^2), x]

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fricas [B]  time = 0.70, size = 120, normalized size = 3.87 \begin {gather*} -2 \, x e^{3} \log \left (\frac {{\left ({\left (x^{2} + 2 \, x + 1\right )} e^{6} \log \left (x^{2}\right )^{2} - 4 \, {\left (x + 1\right )} e^{\left (x^{2} + 6\right )} \log \left (x^{2}\right ) + 4 \, e^{\left (2 \, x^{2} + 6\right )}\right )} e^{\left (-6\right )}}{\log \left (x^{2}\right )^{2}}\right ) + x \log \left (\frac {{\left ({\left (x^{2} + 2 \, x + 1\right )} e^{6} \log \left (x^{2}\right )^{2} - 4 \, {\left (x + 1\right )} e^{\left (x^{2} + 6\right )} \log \left (x^{2}\right ) + 4 \, e^{\left (2 \, x^{2} + 6\right )}\right )} e^{\left (-6\right )}}{\log \left (x^{2}\right )^{2}}\right )^{2} + x e^{6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x+1)*log(x^2)^2-2*exp(x^2)*log(x^2))*log(((x^2+2*x+1)*log(x^2)^2+(-4*x-4)*exp(x^2)*log(x^2)+4*exp
(x^2)^2)/log(x^2)^2)^2+(((-2*x-2)*exp(3)+4*x)*log(x^2)^2+(4*exp(3)-16*x^2)*exp(x^2)*log(x^2)+16*exp(x^2))*log(
((x^2+2*x+1)*log(x^2)^2+(-4*x-4)*exp(x^2)*log(x^2)+4*exp(x^2)^2)/log(x^2)^2)+((x+1)*exp(3)^2-4*x*exp(3))*log(x
^2)^2+(-2*exp(3)^2+16*x^2*exp(3))*exp(x^2)*log(x^2)-16*exp(x^2)*exp(3))/((x+1)*log(x^2)^2-2*exp(x^2)*log(x^2))
,x, algorithm="fricas")

[Out]

-2*x*e^3*log(((x^2 + 2*x + 1)*e^6*log(x^2)^2 - 4*(x + 1)*e^(x^2 + 6)*log(x^2) + 4*e^(2*x^2 + 6))*e^(-6)/log(x^
2)^2) + x*log(((x^2 + 2*x + 1)*e^6*log(x^2)^2 - 4*(x + 1)*e^(x^2 + 6)*log(x^2) + 4*e^(2*x^2 + 6))*e^(-6)/log(x
^2)^2)^2 + x*e^6

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giac [B]  time = 30.32, size = 215, normalized size = 6.94 \begin {gather*} -2 \, x e^{3} \log \left (x^{2} \log \left (x^{2}\right )^{2} - 4 \, x e^{\left (x^{2}\right )} \log \left (x^{2}\right ) + 2 \, x \log \left (x^{2}\right )^{2} - 4 \, e^{\left (x^{2}\right )} \log \left (x^{2}\right ) + \log \left (x^{2}\right )^{2} + 4 \, e^{\left (2 \, x^{2}\right )}\right ) + x \log \left (x^{2} \log \left (x^{2}\right )^{2} - 4 \, x e^{\left (x^{2}\right )} \log \left (x^{2}\right ) + 2 \, x \log \left (x^{2}\right )^{2} - 4 \, e^{\left (x^{2}\right )} \log \left (x^{2}\right ) + \log \left (x^{2}\right )^{2} + 4 \, e^{\left (2 \, x^{2}\right )}\right )^{2} + 2 \, x e^{3} \log \left (\log \left (x^{2}\right )^{2}\right ) - 2 \, x \log \left (x^{2} \log \left (x^{2}\right )^{2} - 4 \, x e^{\left (x^{2}\right )} \log \left (x^{2}\right ) + 2 \, x \log \left (x^{2}\right )^{2} - 4 \, e^{\left (x^{2}\right )} \log \left (x^{2}\right ) + \log \left (x^{2}\right )^{2} + 4 \, e^{\left (2 \, x^{2}\right )}\right ) \log \left (\log \left (x^{2}\right )^{2}\right ) + x \log \left (\log \left (x^{2}\right )^{2}\right )^{2} + x e^{6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x+1)*log(x^2)^2-2*exp(x^2)*log(x^2))*log(((x^2+2*x+1)*log(x^2)^2+(-4*x-4)*exp(x^2)*log(x^2)+4*exp
(x^2)^2)/log(x^2)^2)^2+(((-2*x-2)*exp(3)+4*x)*log(x^2)^2+(4*exp(3)-16*x^2)*exp(x^2)*log(x^2)+16*exp(x^2))*log(
((x^2+2*x+1)*log(x^2)^2+(-4*x-4)*exp(x^2)*log(x^2)+4*exp(x^2)^2)/log(x^2)^2)+((x+1)*exp(3)^2-4*x*exp(3))*log(x
^2)^2+(-2*exp(3)^2+16*x^2*exp(3))*exp(x^2)*log(x^2)-16*exp(x^2)*exp(3))/((x+1)*log(x^2)^2-2*exp(x^2)*log(x^2))
,x, algorithm="giac")

[Out]

-2*x*e^3*log(x^2*log(x^2)^2 - 4*x*e^(x^2)*log(x^2) + 2*x*log(x^2)^2 - 4*e^(x^2)*log(x^2) + log(x^2)^2 + 4*e^(2
*x^2)) + x*log(x^2*log(x^2)^2 - 4*x*e^(x^2)*log(x^2) + 2*x*log(x^2)^2 - 4*e^(x^2)*log(x^2) + log(x^2)^2 + 4*e^
(2*x^2))^2 + 2*x*e^3*log(log(x^2)^2) - 2*x*log(x^2*log(x^2)^2 - 4*x*e^(x^2)*log(x^2) + 2*x*log(x^2)^2 - 4*e^(x
^2)*log(x^2) + log(x^2)^2 + 4*e^(2*x^2))*log(log(x^2)^2) + x*log(log(x^2)^2)^2 + x*e^6

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maple [C]  time = 2.70, size = 22674, normalized size = 731.42

method	result	size
risch	\(\text {Expression too large to display}\)	\(22674\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((x+1)*ln(x^2)^2-2*exp(x^2)*ln(x^2))*ln(((x^2+2*x+1)*ln(x^2)^2+(-4*x-4)*exp(x^2)*ln(x^2)+4*exp(x^2)^2)/ln
(x^2)^2)^2+(((-2*x-2)*exp(3)+4*x)*ln(x^2)^2+(4*exp(3)-16*x^2)*exp(x^2)*ln(x^2)+16*exp(x^2))*ln(((x^2+2*x+1)*ln
(x^2)^2+(-4*x-4)*exp(x^2)*ln(x^2)+4*exp(x^2)^2)/ln(x^2)^2)+((x+1)*exp(3)^2-4*x*exp(3))*ln(x^2)^2+(-2*exp(3)^2+
16*x^2*exp(3))*exp(x^2)*ln(x^2)-16*exp(x^2)*exp(3))/((x+1)*ln(x^2)^2-2*exp(x^2)*ln(x^2)),x,method=_RETURNVERBO
SE)

[Out]

result too large to display

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maxima [B]  time = 0.44, size = 65, normalized size = 2.10 \begin {gather*} 4 \, x \log \left (-{\left (x + 1\right )} \log \relax (x) + e^{\left (x^{2}\right )}\right )^{2} + 4 \, x e^{3} \log \left (\log \relax (x)\right ) + 4 \, x \log \left (\log \relax (x)\right )^{2} + x e^{6} - 4 \, {\left (x e^{3} + 2 \, x \log \left (\log \relax (x)\right )\right )} \log \left (-{\left (x + 1\right )} \log \relax (x) + e^{\left (x^{2}\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x+1)*log(x^2)^2-2*exp(x^2)*log(x^2))*log(((x^2+2*x+1)*log(x^2)^2+(-4*x-4)*exp(x^2)*log(x^2)+4*exp
(x^2)^2)/log(x^2)^2)^2+(((-2*x-2)*exp(3)+4*x)*log(x^2)^2+(4*exp(3)-16*x^2)*exp(x^2)*log(x^2)+16*exp(x^2))*log(
((x^2+2*x+1)*log(x^2)^2+(-4*x-4)*exp(x^2)*log(x^2)+4*exp(x^2)^2)/log(x^2)^2)+((x+1)*exp(3)^2-4*x*exp(3))*log(x
^2)^2+(-2*exp(3)^2+16*x^2*exp(3))*exp(x^2)*log(x^2)-16*exp(x^2)*exp(3))/((x+1)*log(x^2)^2-2*exp(x^2)*log(x^2))
,x, algorithm="maxima")

[Out]

4*x*log(-(x + 1)*log(x) + e^(x^2))^2 + 4*x*e^3*log(log(x)) + 4*x*log(log(x))^2 + x*e^6 - 4*(x*e^3 + 2*x*log(lo
g(x)))*log(-(x + 1)*log(x) + e^(x^2))

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mupad [B]  time = 4.16, size = 56, normalized size = 1.81 \begin {gather*} x\,{\left ({\mathrm {e}}^3-\ln \left (\frac {\left (x^2+2\,x+1\right )\,{\ln \left (x^2\right )}^2-{\mathrm {e}}^{x^2}\,\left (4\,x+4\right )\,\ln \left (x^2\right )+4\,{\mathrm {e}}^{2\,x^2}}{{\ln \left (x^2\right )}^2}\right )\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(16*exp(x^2)*exp(3) + log(x^2)^2*(4*x*exp(3) - exp(6)*(x + 1)) - log((4*exp(2*x^2) + log(x^2)^2*(2*x + x^
2 + 1) - log(x^2)*exp(x^2)*(4*x + 4))/log(x^2)^2)*(16*exp(x^2) + log(x^2)^2*(4*x - exp(3)*(2*x + 2)) + log(x^2
)*exp(x^2)*(4*exp(3) - 16*x^2)) - log((4*exp(2*x^2) + log(x^2)^2*(2*x + x^2 + 1) - log(x^2)*exp(x^2)*(4*x + 4)
)/log(x^2)^2)^2*(log(x^2)^2*(x + 1) - 2*log(x^2)*exp(x^2)) + log(x^2)*exp(x^2)*(2*exp(6) - 16*x^2*exp(3)))/(lo
g(x^2)^2*(x + 1) - 2*log(x^2)*exp(x^2)),x)

[Out]

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

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sympy [B]  time = 1.56, size = 112, normalized size = 3.61 \begin {gather*} x \log {\left (\frac {\left (- 4 x - 4\right ) e^{x^{2}} \log {\left (x^{2} \right )} + \left (x^{2} + 2 x + 1\right ) \log {\left (x^{2} \right )}^{2} + 4 e^{2 x^{2}}}{\log {\left (x^{2} \right )}^{2}} \right )}^{2} - 2 x e^{3} \log {\left (\frac {\left (- 4 x - 4\right ) e^{x^{2}} \log {\left (x^{2} \right )} + \left (x^{2} + 2 x + 1\right ) \log {\left (x^{2} \right )}^{2} + 4 e^{2 x^{2}}}{\log {\left (x^{2} \right )}^{2}} \right )} + x e^{6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x+1)*ln(x**2)**2-2*exp(x**2)*ln(x**2))*ln(((x**2+2*x+1)*ln(x**2)**2+(-4*x-4)*exp(x**2)*ln(x**2)+4
*exp(x**2)**2)/ln(x**2)**2)**2+(((-2*x-2)*exp(3)+4*x)*ln(x**2)**2+(4*exp(3)-16*x**2)*exp(x**2)*ln(x**2)+16*exp
(x**2))*ln(((x**2+2*x+1)*ln(x**2)**2+(-4*x-4)*exp(x**2)*ln(x**2)+4*exp(x**2)**2)/ln(x**2)**2)+((x+1)*exp(3)**2
-4*x*exp(3))*ln(x**2)**2+(-2*exp(3)**2+16*x**2*exp(3))*exp(x**2)*ln(x**2)-16*exp(x**2)*exp(3))/((x+1)*ln(x**2)
**2-2*exp(x**2)*ln(x**2)),x)

[Out]

x*log(((-4*x - 4)*exp(x**2)*log(x**2) + (x**2 + 2*x + 1)*log(x**2)**2 + 4*exp(2*x**2))/log(x**2)**2)**2 - 2*x*
exp(3)*log(((-4*x - 4)*exp(x**2)*log(x**2) + (x**2 + 2*x + 1)*log(x**2)**2 + 4*exp(2*x**2))/log(x**2)**2) + x*
exp(6)

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