3.15.81 \(\int (2 x+e^{4 x+4 x^2+4 e^x x^2+4 (x+e^x x) \log ^2(x)} (4+8 x+e^x (8 x+4 x^2)+(8+8 e^x) \log (x)+(4+e^x (4+4 x)) \log ^2(x))+e^{2 x+2 x^2+2 e^x x^2+2 (x+e^x x) \log ^2(x)} (-2-4 x-8 x^2+e^x (-8 x^2-4 x^3)+(-8 x-8 e^x x) \log (x)+(-4 x+e^x (-4 x-4 x^2)) \log ^2(x))) \, dx\)

Optimal. Leaf size=28 \[ \left (e^{2 x-2 \left (-1-e^x\right ) x \left (x+\log ^2(x)\right )}-x\right )^2 \]

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Rubi [F]  time = 10.19, 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 \left (2 x+\exp \left (4 x+4 x^2+4 e^x x^2+4 \left (x+e^x x\right ) \log ^2(x)\right ) \left (4+8 x+e^x \left (8 x+4 x^2\right )+\left (8+8 e^x\right ) \log (x)+\left (4+e^x (4+4 x)\right ) \log ^2(x)\right )+\exp \left (2 x+2 x^2+2 e^x x^2+2 \left (x+e^x x\right ) \log ^2(x)\right ) \left (-2-4 x-8 x^2+e^x \left (-8 x^2-4 x^3\right )+\left (-8 x-8 e^x x\right ) \log (x)+\left (-4 x+e^x \left (-4 x-4 x^2\right )\right ) \log ^2(x)\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[2*x + E^(4*x + 4*x^2 + 4*E^x*x^2 + 4*(x + E^x*x)*Log[x]^2)*(4 + 8*x + E^x*(8*x + 4*x^2) + (8 + 8*E^x)*Log[
x] + (4 + E^x*(4 + 4*x))*Log[x]^2) + E^(2*x + 2*x^2 + 2*E^x*x^2 + 2*(x + E^x*x)*Log[x]^2)*(-2 - 4*x - 8*x^2 +
E^x*(-8*x^2 - 4*x^3) + (-8*x - 8*E^x*x)*Log[x] + (-4*x + E^x*(-4*x - 4*x^2))*Log[x]^2),x]

[Out]

x^2 - (2*E^(2*x + 2*x^2 + 2*E^x*x^2 + 2*(x + E^x*x)*Log[x]^2)*(x + 2*x^2 + E^x*(2*x^2 + x^3) + 2*(x + E^x*x)*L
og[x] + (x + E^x*(x + x^2))*Log[x]^2))/(1 + 2*x + 2*E^x*x + E^x*x^2 + (2*(x + E^x*x)*Log[x])/x + (1 + E^x + E^
x*x)*Log[x]^2) + 4*Defer[Int][E^(4*x*(1 + x + E^x*x + Log[x]^2 + E^x*Log[x]^2)), x] + 8*Defer[Int][E^(4*x*(1 +
x + E^x*x + Log[x]^2 + E^x*Log[x]^2))*x, x] + 8*Defer[Int][E^(x + 4*x*(1 + x + E^x*x + Log[x]^2 + E^x*Log[x]^
2))*x, x] + 4*Defer[Int][E^(x + 4*x*(1 + x + E^x*x + Log[x]^2 + E^x*Log[x]^2))*x^2, x] + 8*Defer[Int][E^(4*x*(
1 + x + E^x*x + Log[x]^2 + E^x*Log[x]^2))*Log[x], x] + 8*Defer[Int][E^(x + 4*x*(1 + x + E^x*x + Log[x]^2 + E^x
*Log[x]^2))*Log[x], x] + 4*Defer[Int][E^(4*x*(1 + x + E^x*x + Log[x]^2 + E^x*Log[x]^2))*Log[x]^2, x] + 4*Defer
[Int][E^(x + 4*x*(1 + x + E^x*x + Log[x]^2 + E^x*Log[x]^2))*Log[x]^2, x] + 4*Defer[Int][E^(x + 4*x*(1 + x + E^
x*x + Log[x]^2 + E^x*Log[x]^2))*x*Log[x]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x^2+\int \exp \left (4 x+4 x^2+4 e^x x^2+4 \left (x+e^x x\right ) \log ^2(x)\right ) \left (4+8 x+e^x \left (8 x+4 x^2\right )+\left (8+8 e^x\right ) \log (x)+\left (4+e^x (4+4 x)\right ) \log ^2(x)\right ) \, dx+\int \exp \left (2 x+2 x^2+2 e^x x^2+2 \left (x+e^x x\right ) \log ^2(x)\right ) \left (-2-4 x-8 x^2+e^x \left (-8 x^2-4 x^3\right )+\left (-8 x-8 e^x x\right ) \log (x)+\left (-4 x+e^x \left (-4 x-4 x^2\right )\right ) \log ^2(x)\right ) \, dx\\ &=x^2-\frac {2 \exp \left (2 x+2 x^2+2 e^x x^2+2 \left (x+e^x x\right ) \log ^2(x)\right ) \left (x+2 x^2+e^x \left (2 x^2+x^3\right )+2 \left (x+e^x x\right ) \log (x)+\left (x+e^x \left (x+x^2\right )\right ) \log ^2(x)\right )}{1+2 x+2 e^x x+e^x x^2+\frac {2 \left (x+e^x x\right ) \log (x)}{x}+\left (1+e^x+e^x x\right ) \log ^2(x)}+\int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \left (4+8 x+e^x \left (8 x+4 x^2\right )+\left (8+8 e^x\right ) \log (x)+\left (4+e^x (4+4 x)\right ) \log ^2(x)\right ) \, dx\\ &=x^2-\frac {2 \exp \left (2 x+2 x^2+2 e^x x^2+2 \left (x+e^x x\right ) \log ^2(x)\right ) \left (x+2 x^2+e^x \left (2 x^2+x^3\right )+2 \left (x+e^x x\right ) \log (x)+\left (x+e^x \left (x+x^2\right )\right ) \log ^2(x)\right )}{1+2 x+2 e^x x+e^x x^2+\frac {2 \left (x+e^x x\right ) \log (x)}{x}+\left (1+e^x+e^x x\right ) \log ^2(x)}+\int \left (4 e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )}+8 e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} x+4 \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x (2+x)+8 e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \left (1+e^x\right ) \log (x)+4 e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \left (1+e^x+e^x x\right ) \log ^2(x)\right ) \, dx\\ &=x^2-\frac {2 \exp \left (2 x+2 x^2+2 e^x x^2+2 \left (x+e^x x\right ) \log ^2(x)\right ) \left (x+2 x^2+e^x \left (2 x^2+x^3\right )+2 \left (x+e^x x\right ) \log (x)+\left (x+e^x \left (x+x^2\right )\right ) \log ^2(x)\right )}{1+2 x+2 e^x x+e^x x^2+\frac {2 \left (x+e^x x\right ) \log (x)}{x}+\left (1+e^x+e^x x\right ) \log ^2(x)}+4 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \, dx+4 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x (2+x) \, dx+4 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \left (1+e^x+e^x x\right ) \log ^2(x) \, dx+8 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} x \, dx+8 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \left (1+e^x\right ) \log (x) \, dx\\ &=x^2-\frac {2 \exp \left (2 x+2 x^2+2 e^x x^2+2 \left (x+e^x x\right ) \log ^2(x)\right ) \left (x+2 x^2+e^x \left (2 x^2+x^3\right )+2 \left (x+e^x x\right ) \log (x)+\left (x+e^x \left (x+x^2\right )\right ) \log ^2(x)\right )}{1+2 x+2 e^x x+e^x x^2+\frac {2 \left (x+e^x x\right ) \log (x)}{x}+\left (1+e^x+e^x x\right ) \log ^2(x)}+4 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \, dx+4 \int \left (2 \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x+\exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x^2\right ) \, dx+4 \int \left (e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \log ^2(x)+\exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) (1+x) \log ^2(x)\right ) \, dx+8 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} x \, dx+8 \int \left (e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \log (x)+\exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) \log (x)\right ) \, dx\\ &=x^2-\frac {2 \exp \left (2 x+2 x^2+2 e^x x^2+2 \left (x+e^x x\right ) \log ^2(x)\right ) \left (x+2 x^2+e^x \left (2 x^2+x^3\right )+2 \left (x+e^x x\right ) \log (x)+\left (x+e^x \left (x+x^2\right )\right ) \log ^2(x)\right )}{1+2 x+2 e^x x+e^x x^2+\frac {2 \left (x+e^x x\right ) \log (x)}{x}+\left (1+e^x+e^x x\right ) \log ^2(x)}+4 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \, dx+4 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x^2 \, dx+4 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \log ^2(x) \, dx+4 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) (1+x) \log ^2(x) \, dx+8 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} x \, dx+8 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x \, dx+8 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \log (x) \, dx+8 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) \log (x) \, dx\\ &=x^2-\frac {2 \exp \left (2 x+2 x^2+2 e^x x^2+2 \left (x+e^x x\right ) \log ^2(x)\right ) \left (x+2 x^2+e^x \left (2 x^2+x^3\right )+2 \left (x+e^x x\right ) \log (x)+\left (x+e^x \left (x+x^2\right )\right ) \log ^2(x)\right )}{1+2 x+2 e^x x+e^x x^2+\frac {2 \left (x+e^x x\right ) \log (x)}{x}+\left (1+e^x+e^x x\right ) \log ^2(x)}+4 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \, dx+4 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x^2 \, dx+4 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \log ^2(x) \, dx+4 \int \left (\exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) \log ^2(x)+\exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x \log ^2(x)\right ) \, dx+8 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} x \, dx+8 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x \, dx+8 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \log (x) \, dx+8 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) \log (x) \, dx\\ &=x^2-\frac {2 \exp \left (2 x+2 x^2+2 e^x x^2+2 \left (x+e^x x\right ) \log ^2(x)\right ) \left (x+2 x^2+e^x \left (2 x^2+x^3\right )+2 \left (x+e^x x\right ) \log (x)+\left (x+e^x \left (x+x^2\right )\right ) \log ^2(x)\right )}{1+2 x+2 e^x x+e^x x^2+\frac {2 \left (x+e^x x\right ) \log (x)}{x}+\left (1+e^x+e^x x\right ) \log ^2(x)}+4 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \, dx+4 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x^2 \, dx+4 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \log ^2(x) \, dx+4 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) \log ^2(x) \, dx+4 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x \log ^2(x) \, dx+8 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} x \, dx+8 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) x \, dx+8 \int e^{4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )} \log (x) \, dx+8 \int \exp \left (x+4 x \left (1+x+e^x x+\log ^2(x)+e^x \log ^2(x)\right )\right ) \log (x) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 7.53, size = 29, normalized size = 1.04 \begin {gather*} \left (e^{2 x \left (1+x+e^x x+\left (1+e^x\right ) \log ^2(x)\right )}-x\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*x + E^(4*x + 4*x^2 + 4*E^x*x^2 + 4*(x + E^x*x)*Log[x]^2)*(4 + 8*x + E^x*(8*x + 4*x^2) + (8 + 8*E^x
)*Log[x] + (4 + E^x*(4 + 4*x))*Log[x]^2) + E^(2*x + 2*x^2 + 2*E^x*x^2 + 2*(x + E^x*x)*Log[x]^2)*(-2 - 4*x - 8*
x^2 + E^x*(-8*x^2 - 4*x^3) + (-8*x - 8*E^x*x)*Log[x] + (-4*x + E^x*(-4*x - 4*x^2))*Log[x]^2),x]

[Out]

(E^(2*x*(1 + x + E^x*x + (1 + E^x)*Log[x]^2)) - x)^2

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fricas [B]  time = 0.75, size = 65, normalized size = 2.32 \begin {gather*} x^{2} - 2 \, x e^{\left (2 \, x^{2} e^{x} + 2 \, {\left (x e^{x} + x\right )} \log \relax (x)^{2} + 2 \, x^{2} + 2 \, x\right )} + e^{\left (4 \, x^{2} e^{x} + 4 \, {\left (x e^{x} + x\right )} \log \relax (x)^{2} + 4 \, x^{2} + 4 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x+4)*exp(x)+4)*log(x)^2+(8*exp(x)+8)*log(x)+(4*x^2+8*x)*exp(x)+8*x+4)*exp((exp(x)*x+x)*log(x)^2
+exp(x)*x^2+x^2+x)^4+(((-4*x^2-4*x)*exp(x)-4*x)*log(x)^2+(-8*exp(x)*x-8*x)*log(x)+(-4*x^3-8*x^2)*exp(x)-8*x^2-
4*x-2)*exp((exp(x)*x+x)*log(x)^2+exp(x)*x^2+x^2+x)^2+2*x,x, algorithm="fricas")

[Out]

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

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 4 \, {\left ({\left ({\left (x + 1\right )} e^{x} + 1\right )} \log \relax (x)^{2} + {\left (x^{2} + 2 \, x\right )} e^{x} + 2 \, {\left (e^{x} + 1\right )} \log \relax (x) + 2 \, x + 1\right )} e^{\left (4 \, x^{2} e^{x} + 4 \, {\left (x e^{x} + x\right )} \log \relax (x)^{2} + 4 \, x^{2} + 4 \, x\right )} - 2 \, {\left (2 \, {\left ({\left (x^{2} + x\right )} e^{x} + x\right )} \log \relax (x)^{2} + 4 \, x^{2} + 2 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{x} + 4 \, {\left (x e^{x} + x\right )} \log \relax (x) + 2 \, x + 1\right )} e^{\left (2 \, x^{2} e^{x} + 2 \, {\left (x e^{x} + x\right )} \log \relax (x)^{2} + 2 \, x^{2} + 2 \, x\right )} + 2 \, x\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x+4)*exp(x)+4)*log(x)^2+(8*exp(x)+8)*log(x)+(4*x^2+8*x)*exp(x)+8*x+4)*exp((exp(x)*x+x)*log(x)^2
+exp(x)*x^2+x^2+x)^4+(((-4*x^2-4*x)*exp(x)-4*x)*log(x)^2+(-8*exp(x)*x-8*x)*log(x)+(-4*x^3-8*x^2)*exp(x)-8*x^2-
4*x-2)*exp((exp(x)*x+x)*log(x)^2+exp(x)*x^2+x^2+x)^2+2*x,x, algorithm="giac")

[Out]

integrate(4*(((x + 1)*e^x + 1)*log(x)^2 + (x^2 + 2*x)*e^x + 2*(e^x + 1)*log(x) + 2*x + 1)*e^(4*x^2*e^x + 4*(x*
e^x + x)*log(x)^2 + 4*x^2 + 4*x) - 2*(2*((x^2 + x)*e^x + x)*log(x)^2 + 4*x^2 + 2*(x^3 + 2*x^2)*e^x + 4*(x*e^x
+ x)*log(x) + 2*x + 1)*e^(2*x^2*e^x + 2*(x*e^x + x)*log(x)^2 + 2*x^2 + 2*x) + 2*x, x)

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maple [A]  time = 0.17, size = 52, normalized size = 1.86

method	result	size
risch	\({\mathrm e}^{4 x \left ({\mathrm e}^{x} \ln \relax (x )^{2}+\ln \relax (x )^{2}+{\mathrm e}^{x} x +x +1\right )}-2 \,{\mathrm e}^{2 x \left ({\mathrm e}^{x} \ln \relax (x )^{2}+\ln \relax (x )^{2}+{\mathrm e}^{x} x +x +1\right )} x +x^{2}\)	\(52\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((4*x+4)*exp(x)+4)*ln(x)^2+(8*exp(x)+8)*ln(x)+(4*x^2+8*x)*exp(x)+8*x+4)*exp((exp(x)*x+x)*ln(x)^2+exp(x)*x
^2+x^2+x)^4+(((-4*x^2-4*x)*exp(x)-4*x)*ln(x)^2+(-8*exp(x)*x-8*x)*ln(x)+(-4*x^3-8*x^2)*exp(x)-8*x^2-4*x-2)*exp(
(exp(x)*x+x)*ln(x)^2+exp(x)*x^2+x^2+x)^2+2*x,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [B]  time = 0.88, size = 73, normalized size = 2.61 \begin {gather*} x^{2} - 2 \, x e^{\left (2 \, x e^{x} \log \relax (x)^{2} + 2 \, x^{2} e^{x} + 2 \, x \log \relax (x)^{2} + 2 \, x^{2} + 2 \, x\right )} + e^{\left (4 \, x e^{x} \log \relax (x)^{2} + 4 \, x^{2} e^{x} + 4 \, x \log \relax (x)^{2} + 4 \, x^{2} + 4 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x+4)*exp(x)+4)*log(x)^2+(8*exp(x)+8)*log(x)+(4*x^2+8*x)*exp(x)+8*x+4)*exp((exp(x)*x+x)*log(x)^2
+exp(x)*x^2+x^2+x)^4+(((-4*x^2-4*x)*exp(x)-4*x)*log(x)^2+(-8*exp(x)*x-8*x)*log(x)+(-4*x^3-8*x^2)*exp(x)-8*x^2-
4*x-2)*exp((exp(x)*x+x)*log(x)^2+exp(x)*x^2+x^2+x)^2+2*x,x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 1.33, size = 80, normalized size = 2.86 \begin {gather*} x^2+{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^x\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{4\,x\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{4\,x^2}-2\,x\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{2\,x\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{2\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x - exp(2*x + 2*x^2*exp(x) + 2*log(x)^2*(x + x*exp(x)) + 2*x^2)*(4*x + exp(x)*(8*x^2 + 4*x^3) + log(x)*(
8*x + 8*x*exp(x)) + log(x)^2*(4*x + exp(x)*(4*x + 4*x^2)) + 8*x^2 + 2) + exp(4*x + 4*x^2*exp(x) + 4*log(x)^2*(
x + x*exp(x)) + 4*x^2)*(8*x + log(x)^2*(exp(x)*(4*x + 4) + 4) + exp(x)*(8*x + 4*x^2) + log(x)*(8*exp(x) + 8) +
4),x)

[Out]

x^2 + exp(4*x)*exp(4*x*exp(x)*log(x)^2)*exp(4*x^2*exp(x))*exp(4*x*log(x)^2)*exp(4*x^2) - 2*x*exp(2*x)*exp(2*x*
exp(x)*log(x)^2)*exp(2*x^2*exp(x))*exp(2*x*log(x)^2)*exp(2*x^2)

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sympy [B]  time = 3.18, size = 70, normalized size = 2.50 \begin {gather*} x^{2} - 2 x e^{2 x^{2} e^{x} + 2 x^{2} + 2 x + 2 \left (x e^{x} + x\right ) \log {\relax (x )}^{2}} + e^{4 x^{2} e^{x} + 4 x^{2} + 4 x + 4 \left (x e^{x} + x\right ) \log {\relax (x )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x+4)*exp(x)+4)*ln(x)**2+(8*exp(x)+8)*ln(x)+(4*x**2+8*x)*exp(x)+8*x+4)*exp((exp(x)*x+x)*ln(x)**2
+exp(x)*x**2+x**2+x)**4+(((-4*x**2-4*x)*exp(x)-4*x)*ln(x)**2+(-8*exp(x)*x-8*x)*ln(x)+(-4*x**3-8*x**2)*exp(x)-8
*x**2-4*x-2)*exp((exp(x)*x+x)*ln(x)**2+exp(x)*x**2+x**2+x)**2+2*x,x)

[Out]

x**2 - 2*x*exp(2*x**2*exp(x) + 2*x**2 + 2*x + 2*(x*exp(x) + x)*log(x)**2) + exp(4*x**2*exp(x) + 4*x**2 + 4*x +
4*(x*exp(x) + x)*log(x)**2)

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