\(\int \frac {e^{\frac {1}{25} (25 x^2+10 x \log (\log (x^2))+\log ^2(\log (x^2)))} (60 x+20 x^2+(-25 x+150 x^2+50 x^3) \log (x^2)+(12+4 x+(30 x+10 x^2) \log (x^2)) \log (\log (x^2)))}{(225 x+150 x^2+25 x^3) \log (x^2)} \, dx\) [10082]

Optimal result

Integrand size = 103, antiderivative size = 21 \[ \int \frac {e^{\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )} \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{\left (225 x+150 x^2+25 x^3\right ) \log \left (x^2\right )} \, dx=\frac {e^{\left (x+\frac {1}{5} \log \left (\log \left (x^2\right )\right )\right )^2}}{3+x} \]

[Out]

exp((x+1/5*ln(ln(x^2)))^2)/(3+x)

Rubi [F]

\[ \int \frac {e^{\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )} \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{\left (225 x+150 x^2+25 x^3\right ) \log \left (x^2\right )} \, dx=\int \frac {\exp \left (\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )\right ) \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{\left (225 x+150 x^2+25 x^3\right ) \log \left (x^2\right )} \, dx \]

[In]

Int[(E^((25*x^2 + 10*x*Log[Log[x^2]] + Log[Log[x^2]]^2)/25)*(60*x + 20*x^2 + (-25*x + 150*x^2 + 50*x^3)*Log[x^
2] + (12 + 4*x + (30*x + 10*x^2)*Log[x^2])*Log[Log[x^2]]))/((225*x + 150*x^2 + 25*x^3)*Log[x^2]),x]

[Out]

2*Defer[Int][E^((5*x + Log[Log[x^2]])^2/25), x] - Defer[Int][E^((5*x + Log[Log[x^2]])^2/25)/(3 + x)^2, x] - 6*
Defer[Int][E^((5*x + Log[Log[x^2]])^2/25)/(3 + x), x] + (4*Defer[Int][E^((5*x + Log[Log[x^2]])^2/25)/((3 + x)*
Log[x^2]), x])/5 + (2*Defer[Int][(E^((5*x + Log[Log[x^2]])^2/25)*Log[Log[x^2]])/(3 + x), x])/5 + (4*Defer[Int]
[(E^((5*x + Log[Log[x^2]])^2/25)*Log[Log[x^2]])/(x*Log[x^2]), x])/75 - (4*Defer[Int][(E^((5*x + Log[Log[x^2]])
^2/25)*Log[Log[x^2]])/((3 + x)*Log[x^2]), x])/75

Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )\right ) \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{x \left (225+150 x+25 x^2\right ) \log \left (x^2\right )} \, dx \\ & = \int \frac {\exp \left (\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )\right ) \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{25 x (3+x)^2 \log \left (x^2\right )} \, dx \\ & = \frac {1}{25} \int \frac {\exp \left (\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )\right ) \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{x (3+x)^2 \log \left (x^2\right )} \, dx \\ & = \frac {1}{25} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{x (3+x)^2 \log \left (x^2\right )} \, dx \\ & = \frac {1}{25} \int \left (\frac {5 e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \left (12+4 x-5 \log \left (x^2\right )+30 x \log \left (x^2\right )+10 x^2 \log \left (x^2\right )\right )}{(3+x)^2 \log \left (x^2\right )}+\frac {2 e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \left (2+5 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{x (3+x) \log \left (x^2\right )}\right ) \, dx \\ & = \frac {2}{25} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \left (2+5 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{x (3+x) \log \left (x^2\right )} \, dx+\frac {1}{5} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \left (12+4 x-5 \log \left (x^2\right )+30 x \log \left (x^2\right )+10 x^2 \log \left (x^2\right )\right )}{(3+x)^2 \log \left (x^2\right )} \, dx \\ & = \frac {2}{25} \int \left (\frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \left (2+5 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{3 x \log \left (x^2\right )}-\frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \left (2+5 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{3 (3+x) \log \left (x^2\right )}\right ) \, dx+\frac {1}{5} \int \left (\frac {5 e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \left (-1+6 x+2 x^2\right )}{(3+x)^2}+\frac {4 e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{(3+x) \log \left (x^2\right )}\right ) \, dx \\ & = \frac {2}{75} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \left (2+5 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{x \log \left (x^2\right )} \, dx-\frac {2}{75} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \left (2+5 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right )} \, dx+\frac {4}{5} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{(3+x) \log \left (x^2\right )} \, dx+\int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \left (-1+6 x+2 x^2\right )}{(3+x)^2} \, dx \\ & = \frac {2}{75} \int \left (5 e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )+\frac {2 e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )}{x \log \left (x^2\right )}\right ) \, dx-\frac {2}{75} \int \left (\frac {5 e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} x \log \left (\log \left (x^2\right )\right )}{3+x}+\frac {2 e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right )}\right ) \, dx+\frac {4}{5} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{(3+x) \log \left (x^2\right )} \, dx+\int \left (2 e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}-\frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{(3+x)^2}-\frac {6 e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{3+x}\right ) \, dx \\ & = \frac {4}{75} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )}{x \log \left (x^2\right )} \, dx-\frac {4}{75} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right )} \, dx+\frac {2}{15} \int e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right ) \, dx-\frac {2}{15} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} x \log \left (\log \left (x^2\right )\right )}{3+x} \, dx+\frac {4}{5} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{(3+x) \log \left (x^2\right )} \, dx+2 \int e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \, dx-6 \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{3+x} \, dx-\int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{(3+x)^2} \, dx \\ & = \frac {4}{75} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )}{x \log \left (x^2\right )} \, dx-\frac {4}{75} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right )} \, dx+\frac {2}{15} \int e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right ) \, dx-\frac {2}{15} \int \left (e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )-\frac {3 e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )}{3+x}\right ) \, dx+\frac {4}{5} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{(3+x) \log \left (x^2\right )} \, dx+2 \int e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \, dx-6 \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{3+x} \, dx-\int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{(3+x)^2} \, dx \\ & = \frac {4}{75} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )}{x \log \left (x^2\right )} \, dx-\frac {4}{75} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right )} \, dx+\frac {2}{5} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \log \left (\log \left (x^2\right )\right )}{3+x} \, dx+\frac {4}{5} \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{(3+x) \log \left (x^2\right )} \, dx+2 \int e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2} \, dx-6 \int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{3+x} \, dx-\int \frac {e^{\frac {1}{25} \left (5 x+\log \left (\log \left (x^2\right )\right )\right )^2}}{(3+x)^2} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.11 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.57 \[ \int \frac {e^{\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )} \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{\left (225 x+150 x^2+25 x^3\right ) \log \left (x^2\right )} \, dx=\frac {e^{x^2+\frac {1}{25} \log ^2\left (\log \left (x^2\right )\right )} \log ^{\frac {2 x}{5}}\left (x^2\right )}{3+x} \]

[In]

Integrate[(E^((25*x^2 + 10*x*Log[Log[x^2]] + Log[Log[x^2]]^2)/25)*(60*x + 20*x^2 + (-25*x + 150*x^2 + 50*x^3)*
Log[x^2] + (12 + 4*x + (30*x + 10*x^2)*Log[x^2])*Log[Log[x^2]]))/((225*x + 150*x^2 + 25*x^3)*Log[x^2]),x]

[Out]

(E^(x^2 + Log[Log[x^2]]^2/25)*Log[x^2]^((2*x)/5))/(3 + x)

Maple [A] (verified)

Time = 1.13 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.38

method	result	size
parallelrisch	\(\frac {{\mathrm e}^{\frac {{\ln \left (\ln \left (x^{2}\right )\right )}^{2}}{25}+\frac {2 x \ln \left (\ln \left (x^{2}\right )\right )}{5}+x^{2}}}{3+x}\)	\(29\)

[In]

int((((10*x^2+30*x)*ln(x^2)+4*x+12)*ln(ln(x^2))+(50*x^3+150*x^2-25*x)*ln(x^2)+20*x^2+60*x)*exp(1/25*ln(ln(x^2)
)^2+2/5*x*ln(ln(x^2))+x^2)/(25*x^3+150*x^2+225*x)/ln(x^2),x,method=_RETURNVERBOSE)

[Out]

exp(1/25*ln(ln(x^2))^2+2/5*x*ln(ln(x^2))+x^2)/(3+x)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.33 \[ \int \frac {e^{\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )} \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{\left (225 x+150 x^2+25 x^3\right ) \log \left (x^2\right )} \, dx=\frac {e^{\left (x^{2} + \frac {2}{5} \, x \log \left (\log \left (x^{2}\right )\right ) + \frac {1}{25} \, \log \left (\log \left (x^{2}\right )\right )^{2}\right )}}{x + 3} \]

[In]

integrate((((10*x^2+30*x)*log(x^2)+4*x+12)*log(log(x^2))+(50*x^3+150*x^2-25*x)*log(x^2)+20*x^2+60*x)*exp(1/25*
log(log(x^2))^2+2/5*x*log(log(x^2))+x^2)/(25*x^3+150*x^2+225*x)/log(x^2),x, algorithm="fricas")

[Out]

e^(x^2 + 2/5*x*log(log(x^2)) + 1/25*log(log(x^2))^2)/(x + 3)

Sympy [A] (verification not implemented)

Time = 0.25 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.38 \[ \int \frac {e^{\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )} \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{\left (225 x+150 x^2+25 x^3\right ) \log \left (x^2\right )} \, dx=\frac {e^{x^{2} + \frac {2 x \log {\left (\log {\left (x^{2} \right )} \right )}}{5} + \frac {\log {\left (\log {\left (x^{2} \right )} \right )}^{2}}{25}}}{x + 3} \]

[In]

integrate((((10*x**2+30*x)*ln(x**2)+4*x+12)*ln(ln(x**2))+(50*x**3+150*x**2-25*x)*ln(x**2)+20*x**2+60*x)*exp(1/
25*ln(ln(x**2))**2+2/5*x*ln(ln(x**2))+x**2)/(25*x**3+150*x**2+225*x)/ln(x**2),x)

[Out]

exp(x**2 + 2*x*log(log(x**2))/5 + log(log(x**2))**2/25)/(x + 3)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 42 vs. \(2 (20) = 40\).

Time = 0.39 (sec) , antiderivative size = 42, normalized size of antiderivative = 2.00 \[ \int \frac {e^{\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )} \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{\left (225 x+150 x^2+25 x^3\right ) \log \left (x^2\right )} \, dx=\frac {e^{\left (x^{2} + \frac {2}{5} \, x \log \left (2\right ) + \frac {1}{25} \, \log \left (2\right )^{2} + \frac {2}{5} \, x \log \left (\log \left (x\right )\right ) + \frac {2}{25} \, \log \left (2\right ) \log \left (\log \left (x\right )\right ) + \frac {1}{25} \, \log \left (\log \left (x\right )\right )^{2}\right )}}{x + 3} \]

[In]

integrate((((10*x^2+30*x)*log(x^2)+4*x+12)*log(log(x^2))+(50*x^3+150*x^2-25*x)*log(x^2)+20*x^2+60*x)*exp(1/25*
log(log(x^2))^2+2/5*x*log(log(x^2))+x^2)/(25*x^3+150*x^2+225*x)/log(x^2),x, algorithm="maxima")

[Out]

e^(x^2 + 2/5*x*log(2) + 1/25*log(2)^2 + 2/5*x*log(log(x)) + 2/25*log(2)*log(log(x)) + 1/25*log(log(x))^2)/(x +
3)

Giac [F]

\[ \int \frac {e^{\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )} \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{\left (225 x+150 x^2+25 x^3\right ) \log \left (x^2\right )} \, dx=\int { \frac {{\left (20 \, x^{2} + 25 \, {\left (2 \, x^{3} + 6 \, x^{2} - x\right )} \log \left (x^{2}\right ) + 2 \, {\left (5 \, {\left (x^{2} + 3 \, x\right )} \log \left (x^{2}\right ) + 2 \, x + 6\right )} \log \left (\log \left (x^{2}\right )\right ) + 60 \, x\right )} e^{\left (x^{2} + \frac {2}{5} \, x \log \left (\log \left (x^{2}\right )\right ) + \frac {1}{25} \, \log \left (\log \left (x^{2}\right )\right )^{2}\right )}}{25 \, {\left (x^{3} + 6 \, x^{2} + 9 \, x\right )} \log \left (x^{2}\right )} \,d x } \]

[In]

integrate((((10*x^2+30*x)*log(x^2)+4*x+12)*log(log(x^2))+(50*x^3+150*x^2-25*x)*log(x^2)+20*x^2+60*x)*exp(1/25*
log(log(x^2))^2+2/5*x*log(log(x^2))+x^2)/(25*x^3+150*x^2+225*x)/log(x^2),x, algorithm="giac")

[Out]

undef

Mupad [B] (verification not implemented)

Time = 17.22 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.33 \[ \int \frac {e^{\frac {1}{25} \left (25 x^2+10 x \log \left (\log \left (x^2\right )\right )+\log ^2\left (\log \left (x^2\right )\right )\right )} \left (60 x+20 x^2+\left (-25 x+150 x^2+50 x^3\right ) \log \left (x^2\right )+\left (12+4 x+\left (30 x+10 x^2\right ) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )\right )}{\left (225 x+150 x^2+25 x^3\right ) \log \left (x^2\right )} \, dx=\frac {{\ln \left (x^2\right )}^{\frac {2\,x}{5}}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{\frac {{\ln \left (\ln \left (x^2\right )\right )}^2}{25}}}{x+3} \]

[In]

int((exp(log(log(x^2))^2/25 + (2*x*log(log(x^2)))/5 + x^2)*(60*x + log(x^2)*(150*x^2 - 25*x + 50*x^3) + log(lo
g(x^2))*(4*x + log(x^2)*(30*x + 10*x^2) + 12) + 20*x^2))/(log(x^2)*(225*x + 150*x^2 + 25*x^3)),x)

[Out]

(log(x^2)^((2*x)/5)*exp(x^2)*exp(log(log(x^2))^2/25))/(x + 3)