Integrand size = 50, antiderivative size = 20 \[ \int \frac {1}{64} e^{20+\frac {1}{256} e^{20+4 x+4 x^{12 x}}+4 x+4 x^{12 x}} \left (1+x^{12 x} (12+12 \log (x))\right ) \, dx=e^{\frac {1}{256} e^{20+4 x+4 x^{12 x}}} \] Output:
exp(1/256*exp(exp(12*x*ln(x))+5+x)^4)
Time = 0.39 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {1}{64} e^{20+\frac {1}{256} e^{20+4 x+4 x^{12 x}}+4 x+4 x^{12 x}} \left (1+x^{12 x} (12+12 \log (x))\right ) \, dx=e^{\frac {1}{256} e^{20+4 x+4 x^{12 x}}} \] Input:
Integrate[(E^(20 + E^(20 + 4*x + 4*x^(12*x))/256 + 4*x + 4*x^(12*x))*(1 + x^(12*x)*(12 + 12*Log[x])))/64,x]
Output:
E^(E^(20 + 4*x + 4*x^(12*x))/256)
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
\(\displaystyle \int \frac {1}{64} \exp \left (4 x^{12 x}+\frac {1}{256} e^{4 x^{12 x}+4 x+20}+4 x+20\right ) \left (x^{12 x} (12 \log (x)+12)+1\right ) \, dx\) |
\(\Big \downarrow \) 27 |
\(\displaystyle \frac {1}{64} \int \exp \left (4 x^{12 x}+4 x+\frac {1}{256} e^{4 x^{12 x}+4 x+20}+20\right ) \left (12 (\log (x)+1) x^{12 x}+1\right )dx\) |
\(\Big \downarrow \) 7292 |
\(\displaystyle \frac {1}{64} \int \exp \left (\frac {1}{256} \left (1024 x^{12 x}+1024 x+e^{4 x^{12 x}+4 x+20}+5120\right )\right ) \left (12 (\log (x)+1) x^{12 x}+1\right )dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \frac {1}{64} \int \left (12 \exp \left (\frac {1}{256} \left (1024 x^{12 x}+1024 x+e^{4 x^{12 x}+4 x+20}+5120\right )\right ) (\log (x)+1) x^{12 x}+\exp \left (\frac {1}{256} \left (1024 x^{12 x}+1024 x+e^{4 x^{12 x}+4 x+20}+5120\right )\right )\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle \frac {1}{64} \left (\int \exp \left (\frac {1}{256} \left (1024 x^{12 x}+1024 x+e^{4 x^{12 x}+4 x+20}+5120\right )\right )dx+12 \int \exp \left (\frac {1}{256} \left (1024 x^{12 x}+1024 x+e^{4 x^{12 x}+4 x+20}+5120\right )\right ) x^{12 x}dx-12 \int \frac {\int \exp \left (4 \left (x^{12 x}+x+5\right )+\frac {1}{256} e^{4 \left (x^{12 x}+x+5\right )}\right ) x^{12 x}dx}{x}dx+12 \log (x) \int \exp \left (\frac {1}{256} \left (1024 x^{12 x}+1024 x+e^{4 x^{12 x}+4 x+20}+5120\right )\right ) x^{12 x}dx\right )\) |
Input:
Int[(E^(20 + E^(20 + 4*x + 4*x^(12*x))/256 + 4*x + 4*x^(12*x))*(1 + x^(12* x)*(12 + 12*Log[x])))/64,x]
Output:
$Aborted
Time = 2.35 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80
method | result | size |
derivativedivides | \({\mathrm e}^{\frac {{\mathrm e}^{4 \,{\mathrm e}^{12 x \ln \left (x \right )}+20+4 x}}{256}}\) | \(16\) |
default | \({\mathrm e}^{\frac {{\mathrm e}^{4 \,{\mathrm e}^{12 x \ln \left (x \right )}+20+4 x}}{256}}\) | \(16\) |
parallelrisch | \({\mathrm e}^{\frac {{\mathrm e}^{4 \,{\mathrm e}^{12 x \ln \left (x \right )}+20+4 x}}{256}}\) | \(16\) |
risch | \({\mathrm e}^{\frac {{\mathrm e}^{4 x^{12 x}+20+4 x}}{256}}\) | \(17\) |
Input:
int(1/64*((12*ln(x)+12)*exp(12*x*ln(x))+1)*exp(exp(12*x*ln(x))+5+x)^4*exp( 1/256*exp(exp(12*x*ln(x))+5+x)^4),x,method=_RETURNVERBOSE)
Output:
exp(1/256*exp(exp(12*x*ln(x))+5+x)^4)
Time = 0.10 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {1}{64} e^{20+\frac {1}{256} e^{20+4 x+4 x^{12 x}}+4 x+4 x^{12 x}} \left (1+x^{12 x} (12+12 \log (x))\right ) \, dx=e^{\left (\frac {1}{256} \, e^{\left (4 \, x + 4 \, x^{12 \, x} + 20\right )}\right )} \] Input:
integrate(1/64*((12*log(x)+12)*exp(12*x*log(x))+1)*exp(exp(12*x*log(x))+5+ x)^4*exp(1/256*exp(exp(12*x*log(x))+5+x)^4),x, algorithm="fricas")
Output:
e^(1/256*e^(4*x + 4*x^(12*x) + 20))
Time = 3.49 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {1}{64} e^{20+\frac {1}{256} e^{20+4 x+4 x^{12 x}}+4 x+4 x^{12 x}} \left (1+x^{12 x} (12+12 \log (x))\right ) \, dx=e^{\frac {e^{4 x + 4 e^{12 x \log {\left (x \right )}} + 20}}{256}} \] Input:
integrate(1/64*((12*ln(x)+12)*exp(12*x*ln(x))+1)*exp(exp(12*x*ln(x))+5+x)* *4*exp(1/256*exp(exp(12*x*ln(x))+5+x)**4),x)
Output:
exp(exp(4*x + 4*exp(12*x*log(x)) + 20)/256)
Time = 0.24 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {1}{64} e^{20+\frac {1}{256} e^{20+4 x+4 x^{12 x}}+4 x+4 x^{12 x}} \left (1+x^{12 x} (12+12 \log (x))\right ) \, dx=e^{\left (\frac {1}{256} \, e^{\left (4 \, x + 4 \, x^{12 \, x} + 20\right )}\right )} \] Input:
integrate(1/64*((12*log(x)+12)*exp(12*x*log(x))+1)*exp(exp(12*x*log(x))+5+ x)^4*exp(1/256*exp(exp(12*x*log(x))+5+x)^4),x, algorithm="maxima")
Output:
e^(1/256*e^(4*x + 4*x^(12*x) + 20))
\[ \int \frac {1}{64} e^{20+\frac {1}{256} e^{20+4 x+4 x^{12 x}}+4 x+4 x^{12 x}} \left (1+x^{12 x} (12+12 \log (x))\right ) \, dx=\int { \frac {1}{64} \, {\left (12 \, x^{12 \, x} {\left (\log \left (x\right ) + 1\right )} + 1\right )} e^{\left (4 \, x + 4 \, x^{12 \, x} + \frac {1}{256} \, e^{\left (4 \, x + 4 \, x^{12 \, x} + 20\right )} + 20\right )} \,d x } \] Input:
integrate(1/64*((12*log(x)+12)*exp(12*x*log(x))+1)*exp(exp(12*x*log(x))+5+ x)^4*exp(1/256*exp(exp(12*x*log(x))+5+x)^4),x, algorithm="giac")
Output:
integrate(1/64*(12*x^(12*x)*(log(x) + 1) + 1)*e^(4*x + 4*x^(12*x) + 1/256* e^(4*x + 4*x^(12*x) + 20) + 20), x)
Time = 4.51 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {1}{64} e^{20+\frac {1}{256} e^{20+4 x+4 x^{12 x}}+4 x+4 x^{12 x}} \left (1+x^{12 x} (12+12 \log (x))\right ) \, dx={\mathrm {e}}^{\frac {{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{20}\,{\mathrm {e}}^{4\,x^{12\,x}}}{256}} \] Input:
int((exp(4*x + 4*exp(12*x*log(x)) + 20)*exp(exp(4*x + 4*exp(12*x*log(x)) + 20)/256)*(exp(12*x*log(x))*(12*log(x) + 12) + 1))/64,x)
Output:
exp((exp(4*x)*exp(20)*exp(4*x^(12*x)))/256)
Time = 0.16 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {1}{64} e^{20+\frac {1}{256} e^{20+4 x+4 x^{12 x}}+4 x+4 x^{12 x}} \left (1+x^{12 x} (12+12 \log (x))\right ) \, dx=e^{\frac {e^{4 x^{12 x}+4 x} e^{20}}{256}} \] Input:
int(1/64*((12*log(x)+12)*exp(12*x*log(x))+1)*exp(exp(12*x*log(x))+5+x)^4*e xp(1/256*exp(exp(12*x*log(x))+5+x)^4),x)
Output:
e**((e**(4*x**(12*x) + 4*x)*e**20)/256)