\(\int \frac {-3 x^2+8 x^3+e^{\frac {6 e^{25}}{x^2}} (-12 e^{25} x+2 x^3)+(2 x-4 x^2) \log (4)+e^{\frac {3 e^{25}}{x^2}} (-24 e^{25} x-2 x^2+8 x^3+(12 e^{25}-2 x^2) \log (4))+(2 x-4 x^2+e^{\frac {3 e^{25}}{x^2}} (12 e^{25}-2 x^2)) \log (x)}{x^2} \, dx\) [6673]

Optimal result

Integrand size = 126, antiderivative size = 25 \[ \int \frac {-3 x^2+8 x^3+e^{\frac {6 e^{25}}{x^2}} \left (-12 e^{25} x+2 x^3\right )+\left (2 x-4 x^2\right ) \log (4)+e^{\frac {3 e^{25}}{x^2}} \left (-24 e^{25} x-2 x^2+8 x^3+\left (12 e^{25}-2 x^2\right ) \log (4)\right )+\left (2 x-4 x^2+e^{\frac {3 e^{25}}{x^2}} \left (12 e^{25}-2 x^2\right )\right ) \log (x)}{x^2} \, dx=x+\left (-2 x-e^{\frac {3 e^{25}}{x^2}} x+\log (4)+\log (x)\right )^2 \]

[Out]

(2*ln(2)-2*x-exp(3*exp(25)/x^2)*x+ln(x))^2+x

Rubi [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(80\) vs. \(2(25)=50\).

Time = 0.20 (sec) , antiderivative size = 80, normalized size of antiderivative = 3.20, number of steps used = 11, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {14, 2326, 2388, 2338, 2332} \[ \int \frac {-3 x^2+8 x^3+e^{\frac {6 e^{25}}{x^2}} \left (-12 e^{25} x+2 x^3\right )+\left (2 x-4 x^2\right ) \log (4)+e^{\frac {3 e^{25}}{x^2}} \left (-24 e^{25} x-2 x^2+8 x^3+\left (12 e^{25}-2 x^2\right ) \log (4)\right )+\left (2 x-4 x^2+e^{\frac {3 e^{25}}{x^2}} \left (12 e^{25}-2 x^2\right )\right ) \log (x)}{x^2} \, dx=e^{\frac {6 e^{25}}{x^2}} x^2+4 x^2+2 e^{\frac {3 e^{25}}{x^2}-25} x \left (2 e^{25} x-e^{25} \log (x)-e^{25} \log (4)\right )+4 x+\log ^2(x)-4 x \log (x)-x (3+\log (256))+\log (16) \log (x) \]

[In]

Int[(-3*x^2 + 8*x^3 + E^((6*E^25)/x^2)*(-12*E^25*x + 2*x^3) + (2*x - 4*x^2)*Log[4] + E^((3*E^25)/x^2)*(-24*E^2
5*x - 2*x^2 + 8*x^3 + (12*E^25 - 2*x^2)*Log[4]) + (2*x - 4*x^2 + E^((3*E^25)/x^2)*(12*E^25 - 2*x^2))*Log[x])/x
^2,x]

[Out]

4*x + 4*x^2 + E^((6*E^25)/x^2)*x^2 - x*(3 + Log[256]) - 4*x*Log[x] + Log[16]*Log[x] + Log[x]^2 + 2*E^(-25 + (3
*E^25)/x^2)*x*(2*E^25*x - E^25*Log[4] - E^25*Log[x])

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rule 2326

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = v*(y/(Log[F]*D[u, x]))}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rule 2332

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rule 2338

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, c, n}, x]

Rule 2388

Int[(((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_) + (e_.)*(x_))^(q_.))/(x_), x_Symbol] :> Dist[d, Int[(d
+ e*x)^(q - 1)*((a + b*Log[c*x^n])^p/x), x], x] + Dist[e, Int[(d + e*x)^(q - 1)*(a + b*Log[c*x^n])^p, x], x] /
; FreeQ[{a, b, c, d, e, n}, x] && IGtQ[p, 0] && GtQ[q, 0] && IntegerQ[2*q]

Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {2 e^{\frac {6 e^{25}}{x^2}} \left (-6 e^{25}+x^2\right )}{x}+\frac {8 x^2-3 x \left (1+\frac {4 \log (4)}{3}\right )+\log (16)+2 \log (x)-4 x \log (x)}{x}+\frac {2 e^{\frac {3 e^{25}}{x^2}} \left (-12 e^{25} x+4 x^3+6 e^{25} \log (4)-x^2 (1+\log (4))+6 e^{25} \log (x)-x^2 \log (x)\right )}{x^2}\right ) \, dx \\ & = 2 \int \frac {e^{\frac {6 e^{25}}{x^2}} \left (-6 e^{25}+x^2\right )}{x} \, dx+2 \int \frac {e^{\frac {3 e^{25}}{x^2}} \left (-12 e^{25} x+4 x^3+6 e^{25} \log (4)-x^2 (1+\log (4))+6 e^{25} \log (x)-x^2 \log (x)\right )}{x^2} \, dx+\int \frac {8 x^2-3 x \left (1+\frac {4 \log (4)}{3}\right )+\log (16)+2 \log (x)-4 x \log (x)}{x} \, dx \\ & = e^{\frac {6 e^{25}}{x^2}} x^2+2 e^{-25+\frac {3 e^{25}}{x^2}} x \left (2 e^{25} x-e^{25} \log (4)-e^{25} \log (x)\right )+\int \left (\frac {8 x^2+\log (16)-x (3+\log (256))}{x}-\frac {2 (-1+2 x) \log (x)}{x}\right ) \, dx \\ & = e^{\frac {6 e^{25}}{x^2}} x^2+2 e^{-25+\frac {3 e^{25}}{x^2}} x \left (2 e^{25} x-e^{25} \log (4)-e^{25} \log (x)\right )-2 \int \frac {(-1+2 x) \log (x)}{x} \, dx+\int \frac {8 x^2+\log (16)-x (3+\log (256))}{x} \, dx \\ & = e^{\frac {6 e^{25}}{x^2}} x^2+2 e^{-25+\frac {3 e^{25}}{x^2}} x \left (2 e^{25} x-e^{25} \log (4)-e^{25} \log (x)\right )+2 \int \frac {\log (x)}{x} \, dx-4 \int \log (x) \, dx+\int \left (-3+8 x+\frac {\log (16)}{x}-\log (256)\right ) \, dx \\ & = 4 x+4 x^2+e^{\frac {6 e^{25}}{x^2}} x^2-x (3+\log (256))-4 x \log (x)+\log (16) \log (x)+\log ^2(x)+2 e^{-25+\frac {3 e^{25}}{x^2}} x \left (2 e^{25} x-e^{25} \log (4)-e^{25} \log (x)\right ) \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(64\) vs. \(2(25)=50\).

Time = 0.15 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.56 \[ \int \frac {-3 x^2+8 x^3+e^{\frac {6 e^{25}}{x^2}} \left (-12 e^{25} x+2 x^3\right )+\left (2 x-4 x^2\right ) \log (4)+e^{\frac {3 e^{25}}{x^2}} \left (-24 e^{25} x-2 x^2+8 x^3+\left (12 e^{25}-2 x^2\right ) \log (4)\right )+\left (2 x-4 x^2+e^{\frac {3 e^{25}}{x^2}} \left (12 e^{25}-2 x^2\right )\right ) \log (x)}{x^2} \, dx=x \left (1+\left (2+e^{\frac {3 e^{25}}{x^2}}\right )^2 x-4 \log (4)-2 e^{\frac {3 e^{25}}{x^2}} \log (4)\right )+\left (-2 \left (2+e^{\frac {3 e^{25}}{x^2}}\right ) x+\log (16)\right ) \log (x)+\log ^2(x) \]

[In]

Integrate[(-3*x^2 + 8*x^3 + E^((6*E^25)/x^2)*(-12*E^25*x + 2*x^3) + (2*x - 4*x^2)*Log[4] + E^((3*E^25)/x^2)*(-
24*E^25*x - 2*x^2 + 8*x^3 + (12*E^25 - 2*x^2)*Log[4]) + (2*x - 4*x^2 + E^((3*E^25)/x^2)*(12*E^25 - 2*x^2))*Log
[x])/x^2,x]

[Out]

x*(1 + (2 + E^((3*E^25)/x^2))^2*x - 4*Log[4] - 2*E^((3*E^25)/x^2)*Log[4]) + (-2*(2 + E^((3*E^25)/x^2))*x + Log
[16])*Log[x] + Log[x]^2

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(78\) vs. \(2(25)=50\).

Time = 0.83 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.16

method	result	size
risch	\(\ln \left (x \right )^{2}+\left (-2 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}} x -4 x \right ) \ln \left (x \right )+x^{2} {\mathrm e}^{\frac {6 \,{\mathrm e}^{25}}{x^{2}}}-4 \ln \left (2\right ) x \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}}+4 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}} x^{2}+4 \ln \left (2\right ) \ln \left (x \right )-8 x \ln \left (2\right )+4 x^{2}+x\)	\(79\)
parallelrisch	\(-2 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}} \ln \left (x \right ) x -4 \ln \left (2\right ) x \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}}+4 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}} x^{2}+x^{2} {\mathrm e}^{\frac {6 \,{\mathrm e}^{25}}{x^{2}}}+\ln \left (x \right )^{2}+4 \ln \left (2\right ) \ln \left (x \right )-4 x \ln \left (x \right )-8 x \ln \left (2\right )+4 x^{2}+x\)	\(81\)
default	\(\frac {4 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}} x^{3}-2 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}} \ln \left (x \right ) x^{2}-4 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}} \ln \left (2\right ) x^{2}}{x}+4 x^{2}-8 x \ln \left (2\right )+x +4 \ln \left (2\right ) \ln \left (x \right )+x^{2} {\mathrm e}^{\frac {6 \,{\mathrm e}^{25}}{x^{2}}}+\ln \left (x \right )^{2}-4 x \ln \left (x \right )\)	\(88\)
parts	\(\frac {4 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}} x^{3}-2 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}} \ln \left (x \right ) x^{2}-4 \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{25}}{x^{2}}} \ln \left (2\right ) x^{2}}{x}+4 x^{2}-8 x \ln \left (2\right )+x +4 \ln \left (2\right ) \ln \left (x \right )+x^{2} {\mathrm e}^{\frac {6 \,{\mathrm e}^{25}}{x^{2}}}+\ln \left (x \right )^{2}-4 x \ln \left (x \right )\)	\(88\)

[In]

int((((12*exp(25)-2*x^2)*exp(3*exp(25)/x^2)-4*x^2+2*x)*ln(x)+(-12*x*exp(25)+2*x^3)*exp(3*exp(25)/x^2)^2+(2*(12
*exp(25)-2*x^2)*ln(2)-24*x*exp(25)+8*x^3-2*x^2)*exp(3*exp(25)/x^2)+2*(-4*x^2+2*x)*ln(2)+8*x^3-3*x^2)/x^2,x,met
hod=_RETURNVERBOSE)

[Out]

ln(x)^2+(-2*exp(3*exp(25)/x^2)*x-4*x)*ln(x)+x^2*exp(6*exp(25)/x^2)-4*ln(2)*x*exp(3*exp(25)/x^2)+4*exp(3*exp(25
)/x^2)*x^2+4*ln(2)*ln(x)-8*x*ln(2)+4*x^2+x

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (26) = 52\).

Time = 0.46 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.76 \[ \int \frac {-3 x^2+8 x^3+e^{\frac {6 e^{25}}{x^2}} \left (-12 e^{25} x+2 x^3\right )+\left (2 x-4 x^2\right ) \log (4)+e^{\frac {3 e^{25}}{x^2}} \left (-24 e^{25} x-2 x^2+8 x^3+\left (12 e^{25}-2 x^2\right ) \log (4)\right )+\left (2 x-4 x^2+e^{\frac {3 e^{25}}{x^2}} \left (12 e^{25}-2 x^2\right )\right ) \log (x)}{x^2} \, dx=x^{2} e^{\left (\frac {6 \, e^{25}}{x^{2}}\right )} + 4 \, x^{2} + 4 \, {\left (x^{2} - x \log \left (2\right )\right )} e^{\left (\frac {3 \, e^{25}}{x^{2}}\right )} - 8 \, x \log \left (2\right ) - 2 \, {\left (x e^{\left (\frac {3 \, e^{25}}{x^{2}}\right )} + 2 \, x - 2 \, \log \left (2\right )\right )} \log \left (x\right ) + \log \left (x\right )^{2} + x \]

[In]

integrate((((12*exp(25)-2*x^2)*exp(3*exp(25)/x^2)-4*x^2+2*x)*log(x)+(-12*x*exp(25)+2*x^3)*exp(3*exp(25)/x^2)^2
+(2*(12*exp(25)-2*x^2)*log(2)-24*x*exp(25)+8*x^3-2*x^2)*exp(3*exp(25)/x^2)+2*(-4*x^2+2*x)*log(2)+8*x^3-3*x^2)/
x^2,x, algorithm="fricas")

[Out]

x^2*e^(6*e^25/x^2) + 4*x^2 + 4*(x^2 - x*log(2))*e^(3*e^25/x^2) - 8*x*log(2) - 2*(x*e^(3*e^25/x^2) + 2*x - 2*lo
g(2))*log(x) + log(x)^2 + x

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (26) = 52\).

Time = 0.36 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.00 \[ \int \frac {-3 x^2+8 x^3+e^{\frac {6 e^{25}}{x^2}} \left (-12 e^{25} x+2 x^3\right )+\left (2 x-4 x^2\right ) \log (4)+e^{\frac {3 e^{25}}{x^2}} \left (-24 e^{25} x-2 x^2+8 x^3+\left (12 e^{25}-2 x^2\right ) \log (4)\right )+\left (2 x-4 x^2+e^{\frac {3 e^{25}}{x^2}} \left (12 e^{25}-2 x^2\right )\right ) \log (x)}{x^2} \, dx=x^{2} e^{\frac {6 e^{25}}{x^{2}}} + 4 x^{2} - 4 x \log {\left (x \right )} + x \left (1 - 8 \log {\left (2 \right )}\right ) + \left (4 x^{2} - 2 x \log {\left (x \right )} - 4 x \log {\left (2 \right )}\right ) e^{\frac {3 e^{25}}{x^{2}}} + \log {\left (x \right )}^{2} + 4 \log {\left (2 \right )} \log {\left (x \right )} \]

[In]

integrate((((12*exp(25)-2*x**2)*exp(3*exp(25)/x**2)-4*x**2+2*x)*ln(x)+(-12*x*exp(25)+2*x**3)*exp(3*exp(25)/x**
2)**2+(2*(12*exp(25)-2*x**2)*ln(2)-24*x*exp(25)+8*x**3-2*x**2)*exp(3*exp(25)/x**2)+2*(-4*x**2+2*x)*ln(2)+8*x**
3-3*x**2)/x**2,x)

[Out]

x**2*exp(6*exp(25)/x**2) + 4*x**2 - 4*x*log(x) + x*(1 - 8*log(2)) + (4*x**2 - 2*x*log(x) - 4*x*log(2))*exp(3*e
xp(25)/x**2) + log(x)**2 + 4*log(2)*log(x)

Maxima [F]

\[ \int \frac {-3 x^2+8 x^3+e^{\frac {6 e^{25}}{x^2}} \left (-12 e^{25} x+2 x^3\right )+\left (2 x-4 x^2\right ) \log (4)+e^{\frac {3 e^{25}}{x^2}} \left (-24 e^{25} x-2 x^2+8 x^3+\left (12 e^{25}-2 x^2\right ) \log (4)\right )+\left (2 x-4 x^2+e^{\frac {3 e^{25}}{x^2}} \left (12 e^{25}-2 x^2\right )\right ) \log (x)}{x^2} \, dx=\int { \frac {8 \, x^{3} - 3 \, x^{2} + 2 \, {\left (x^{3} - 6 \, x e^{25}\right )} e^{\left (\frac {6 \, e^{25}}{x^{2}}\right )} + 2 \, {\left (4 \, x^{3} - x^{2} - 12 \, x e^{25} - 2 \, {\left (x^{2} - 6 \, e^{25}\right )} \log \left (2\right )\right )} e^{\left (\frac {3 \, e^{25}}{x^{2}}\right )} - 4 \, {\left (2 \, x^{2} - x\right )} \log \left (2\right ) - 2 \, {\left (2 \, x^{2} + {\left (x^{2} - 6 \, e^{25}\right )} e^{\left (\frac {3 \, e^{25}}{x^{2}}\right )} - x\right )} \log \left (x\right )}{x^{2}} \,d x } \]

[In]

integrate((((12*exp(25)-2*x^2)*exp(3*exp(25)/x^2)-4*x^2+2*x)*log(x)+(-12*x*exp(25)+2*x^3)*exp(3*exp(25)/x^2)^2
+(2*(12*exp(25)-2*x^2)*log(2)-24*x*exp(25)+8*x^3-2*x^2)*exp(3*exp(25)/x^2)+2*(-4*x^2+2*x)*log(2)+8*x^3-3*x^2)/
x^2,x, algorithm="maxima")

[Out]

-2*sqrt(3)*x*sqrt(-e^25/x^2)*gamma(-1/2, -3*e^25/x^2)*log(2) - sqrt(3)*x*sqrt(-e^25/x^2)*gamma(-1/2, -3*e^25/x
^2) - 2*x*e^(3*e^25/x^2)*log(x) - 4*sqrt(3)*sqrt(pi)*(erf(sqrt(3)*sqrt(-e^25/x^2)) - 1)*e^25*log(2)/(x*sqrt(-e
^25/x^2)) + 4*x^2 + 6*Ei(6*e^25/x^2)*e^25 + 12*Ei(3*e^25/x^2)*e^25 - 12*e^25*gamma(-1, -3*e^25/x^2) - 6*e^25*g
amma(-1, -6*e^25/x^2) - 8*x*log(2) - 4*x*log(x) + 4*log(2)*log(x) + log(x)^2 + x + 2*integrate(e^(3*e^25/x^2),
x)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 126 vs. \(2 (26) = 52\).

Time = 0.31 (sec) , antiderivative size = 126, normalized size of antiderivative = 5.04 \[ \int \frac {-3 x^2+8 x^3+e^{\frac {6 e^{25}}{x^2}} \left (-12 e^{25} x+2 x^3\right )+\left (2 x-4 x^2\right ) \log (4)+e^{\frac {3 e^{25}}{x^2}} \left (-24 e^{25} x-2 x^2+8 x^3+\left (12 e^{25}-2 x^2\right ) \log (4)\right )+\left (2 x-4 x^2+e^{\frac {3 e^{25}}{x^2}} \left (12 e^{25}-2 x^2\right )\right ) \log (x)}{x^2} \, dx=x^{2} e^{\left (\frac {25 \, x^{2} + 6 \, e^{25}}{x^{2}} - 25\right )} + {\left (4 \, x^{2} e^{25} + 4 \, x^{2} e^{\left (\frac {25 \, x^{2} + 3 \, e^{25}}{x^{2}}\right )} - 8 \, x e^{25} \log \left (2\right ) - 4 \, x e^{\left (\frac {25 \, x^{2} + 3 \, e^{25}}{x^{2}}\right )} \log \left (2\right ) - 4 \, x e^{25} \log \left (x\right ) - 2 \, x e^{\left (\frac {25 \, x^{2} + 3 \, e^{25}}{x^{2}}\right )} \log \left (x\right ) + 4 \, e^{25} \log \left (2\right ) \log \left (x\right ) + e^{25} \log \left (x\right )^{2} + x e^{25}\right )} e^{\left (-25\right )} \]

[In]

integrate((((12*exp(25)-2*x^2)*exp(3*exp(25)/x^2)-4*x^2+2*x)*log(x)+(-12*x*exp(25)+2*x^3)*exp(3*exp(25)/x^2)^2
+(2*(12*exp(25)-2*x^2)*log(2)-24*x*exp(25)+8*x^3-2*x^2)*exp(3*exp(25)/x^2)+2*(-4*x^2+2*x)*log(2)+8*x^3-3*x^2)/
x^2,x, algorithm="giac")

[Out]

x^2*e^((25*x^2 + 6*e^25)/x^2 - 25) + (4*x^2*e^25 + 4*x^2*e^((25*x^2 + 3*e^25)/x^2) - 8*x*e^25*log(2) - 4*x*e^(
(25*x^2 + 3*e^25)/x^2)*log(2) - 4*x*e^25*log(x) - 2*x*e^((25*x^2 + 3*e^25)/x^2)*log(x) + 4*e^25*log(2)*log(x)
+ e^25*log(x)^2 + x*e^25)*e^(-25)

Mupad [B] (verification not implemented)

Time = 14.47 (sec) , antiderivative size = 78, normalized size of antiderivative = 3.12 \[ \int \frac {-3 x^2+8 x^3+e^{\frac {6 e^{25}}{x^2}} \left (-12 e^{25} x+2 x^3\right )+\left (2 x-4 x^2\right ) \log (4)+e^{\frac {3 e^{25}}{x^2}} \left (-24 e^{25} x-2 x^2+8 x^3+\left (12 e^{25}-2 x^2\right ) \log (4)\right )+\left (2 x-4 x^2+e^{\frac {3 e^{25}}{x^2}} \left (12 e^{25}-2 x^2\right )\right ) \log (x)}{x^2} \, dx=x+4\,x^2\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{25}}{x^2}}+x^2\,{\mathrm {e}}^{\frac {6\,{\mathrm {e}}^{25}}{x^2}}-8\,x\,\ln \left (2\right )+{\ln \left (x\right )}^2+4\,\ln \left (2\right )\,\ln \left (x\right )-4\,x\,\ln \left (x\right )+4\,x^2-4\,x\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{25}}{x^2}}\,\ln \left (2\right )-2\,x\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{25}}{x^2}}\,\ln \left (x\right ) \]

[In]

int((2*log(2)*(2*x - 4*x^2) - exp((6*exp(25))/x^2)*(12*x*exp(25) - 2*x^3) + log(x)*(2*x + exp((3*exp(25))/x^2)
*(12*exp(25) - 2*x^2) - 4*x^2) + exp((3*exp(25))/x^2)*(2*log(2)*(12*exp(25) - 2*x^2) - 24*x*exp(25) - 2*x^2 +
8*x^3) - 3*x^2 + 8*x^3)/x^2,x)

[Out]

x + 4*x^2*exp((3*exp(25))/x^2) + x^2*exp((6*exp(25))/x^2) - 8*x*log(2) + log(x)^2 + 4*log(2)*log(x) - 4*x*log(
x) + 4*x^2 - 4*x*exp((3*exp(25))/x^2)*log(2) - 2*x*exp((3*exp(25))/x^2)*log(x)