3.97.92 \(\int \frac {1}{64} e^{20+\frac {1}{256} e^{20+4 x+4 x^{12 x}}+4 x+4 x^{12 x}} (1+x^{12 x} (12+12 \log (x))) \, dx\)

Optimal. Leaf size=20 \[ e^{\frac {1}{256} e^{20+4 x+4 x^{12 x}}} \]

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Rubi [F]  time = 1.01, 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 {1}{64} \exp \left (20+\frac {1}{256} e^{20+4 x+4 x^{12 x}}+4 x+4 x^{12 x}\right ) \left (1+x^{12 x} (12+12 \log (x))\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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]

[Out]

Defer[Int][E^((5120 + E^(20 + 4*x + 4*x^(12*x)) + 1024*x + 1024*x^(12*x))/256), x]/64 + (3*Defer[Int][E^((5120
+ E^(20 + 4*x + 4*x^(12*x)) + 1024*x + 1024*x^(12*x))/256)*x^(12*x), x])/16 + (3*Log[x]*Defer[Int][E^((5120 +
E^(20 + 4*x + 4*x^(12*x)) + 1024*x + 1024*x^(12*x))/256)*x^(12*x), x])/16 - (3*Defer[Int][Defer[Int][E^(E^(4*
(5 + x + x^(12*x)))/256 + 4*(5 + x + x^(12*x)))*x^(12*x), x]/x, x])/16

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{64} \int \exp \left (20+\frac {1}{256} e^{20+4 x+4 x^{12 x}}+4 x+4 x^{12 x}\right ) \left (1+x^{12 x} (12+12 \log (x))\right ) \, dx\\ &=\frac {1}{64} \int \exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) \left (1+x^{12 x} (12+12 \log (x))\right ) \, dx\\ &=\frac {1}{64} \int \left (\exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right )+12 \exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) x^{12 x} (1+\log (x))\right ) \, dx\\ &=\frac {1}{64} \int \exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) \, dx+\frac {3}{16} \int \exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) x^{12 x} (1+\log (x)) \, dx\\ &=\frac {1}{64} \int \exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) \, dx+\frac {3}{16} \int \left (\exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) x^{12 x}+\exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) x^{12 x} \log (x)\right ) \, dx\\ &=\frac {1}{64} \int \exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) \, dx+\frac {3}{16} \int \exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) x^{12 x} \, dx+\frac {3}{16} \int \exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) x^{12 x} \log (x) \, dx\\ &=\frac {1}{64} \int \exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) \, dx+\frac {3}{16} \int \exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) x^{12 x} \, dx-\frac {3}{16} \int \frac {\int \exp \left (\frac {1}{256} e^{4 \left (5+x+x^{12 x}\right )}+4 \left (5+x+x^{12 x}\right )\right ) x^{12 x} \, dx}{x} \, dx+\frac {1}{16} (3 \log (x)) \int \exp \left (\frac {1}{256} \left (5120+e^{20+4 x+4 x^{12 x}}+1024 x+1024 x^{12 x}\right )\right ) x^{12 x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.35, size = 20, normalized size = 1.00 \begin {gather*} e^{\frac {1}{256} e^{20+4 x+4 x^{12 x}}} \end {gather*}

Antiderivative was successfully verified.

[In]

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]

[Out]

E^(E^(20 + 4*x + 4*x^(12*x))/256)

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fricas [A]  time = 0.72, size = 16, normalized size = 0.80 \begin {gather*} e^{\left (\frac {1}{256} \, e^{\left (4 \, x + 4 \, x^{12 \, x} + 20\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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")

[Out]

e^(1/256*e^(4*x + 4*x^(12*x) + 20))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{64} \, {\left (12 \, x^{12 \, x} {\left (\log \relax (x) + 1\right )} + 1\right )} e^{\left (4 \, x^{12 \, x} + 4 \, x + \frac {1}{256} \, e^{\left (4 \, x + 4 \, x^{12 \, x} + 20\right )} + 20\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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")

[Out]

integrate(1/64*(12*x^(12*x)*(log(x) + 1) + 1)*e^(4*x^(12*x) + 4*x + 1/256*e^(4*x + 4*x^(12*x) + 20) + 20), x)

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maple [A]  time = 0.03, size = 16, normalized size = 0.80

method	result	size
derivativedivides	\({\mathrm e}^{\frac {{\mathrm e}^{4 \,{\mathrm e}^{12 x \ln \relax (x )}+20+4 x}}{256}}\)	\(16\)
default	\({\mathrm e}^{\frac {{\mathrm e}^{4 \,{\mathrm e}^{12 x \ln \relax (x )}+20+4 x}}{256}}\)	\(16\)
risch	\({\mathrm e}^{\frac {{\mathrm e}^{4 x^{12 x}+20+4 x}}{256}}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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)

[Out]

exp(1/256*exp(exp(12*x*ln(x))+5+x)^4)

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maxima [A]  time = 0.57, size = 16, normalized size = 0.80 \begin {gather*} e^{\left (\frac {1}{256} \, e^{\left (4 \, x + 4 \, x^{12 \, x} + 20\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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")

[Out]

e^(1/256*e^(4*x + 4*x^(12*x) + 20))

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mupad [B]  time = 6.21, size = 17, normalized size = 0.85 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{20}\,{\mathrm {e}}^{4\,x^{12\,x}}}{256}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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)

[Out]

exp((exp(4*x)*exp(20)*exp(4*x^(12*x)))/256)

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sympy [A]  time = 3.61, size = 19, normalized size = 0.95 \begin {gather*} e^{\frac {e^{4 x + 4 e^{12 x \log {\relax (x )}} + 20}}{256}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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)

[Out]

exp(exp(4*x + 4*exp(12*x*log(x)) + 20)/256)

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