3.43.51 \(\int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 (-10 x^3-20 x^4-10 x^5+(2 x^2+4 x^3+2 x^4) \log (4)) \log (x)+4 (x^4+4 x^5+6 x^6+4 x^7+x^8) \log ^2(x)} (200 x-40 x^2-80 x^3-40 x^4+(-40+8 x+16 x^2+8 x^3) \log (4)+(-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+(16 x+48 x^2+32 x^3) \log (4)) \log (x)+(16 x^3+80 x^4+144 x^5+112 x^6+32 x^7) \log ^2(x)) \, dx\)

Optimal. Leaf size=22 \[ e^{4 \left (-5 x+\log (4)+\left (x+x^2\right )^2 \log (x)\right )^2} \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(100*x^2 - 40*x*Log[4] + 4*Log[4]^2 + 4*(-10*x^3 - 20*x^4 - 10*x^5 + (2*x^2 + 4*x^3 + 2*x^4)*Log[4])*Log
[x] + 4*(x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8)*Log[x]^2)*(200*x - 40*x^2 - 80*x^3 - 40*x^4 + (-40 + 8*x + 16*x^2
+ 8*x^3)*Log[4] + (-120*x^2 - 312*x^3 - 168*x^4 + 48*x^5 + 32*x^6 + 8*x^7 + (16*x + 48*x^2 + 32*x^3)*Log[4])*L
og[x] + (16*x^3 + 80*x^4 + 144*x^5 + 112*x^6 + 32*x^7)*Log[x]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [F]  time = 2.72, size = 0, normalized size = 0.00 \begin {gather*} \int e^{100 x^2-40 x \log (4)+4 \log ^2(4)+4 \left (-10 x^3-20 x^4-10 x^5+\left (2 x^2+4 x^3+2 x^4\right ) \log (4)\right ) \log (x)+4 \left (x^4+4 x^5+6 x^6+4 x^7+x^8\right ) \log ^2(x)} \left (200 x-40 x^2-80 x^3-40 x^4+\left (-40+8 x+16 x^2+8 x^3\right ) \log (4)+\left (-120 x^2-312 x^3-168 x^4+48 x^5+32 x^6+8 x^7+\left (16 x+48 x^2+32 x^3\right ) \log (4)\right ) \log (x)+\left (16 x^3+80 x^4+144 x^5+112 x^6+32 x^7\right ) \log ^2(x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[E^(100*x^2 - 40*x*Log[4] + 4*Log[4]^2 + 4*(-10*x^3 - 20*x^4 - 10*x^5 + (2*x^2 + 4*x^3 + 2*x^4)*Log[4
])*Log[x] + 4*(x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8)*Log[x]^2)*(200*x - 40*x^2 - 80*x^3 - 40*x^4 + (-40 + 8*x + 1
6*x^2 + 8*x^3)*Log[4] + (-120*x^2 - 312*x^3 - 168*x^4 + 48*x^5 + 32*x^6 + 8*x^7 + (16*x + 48*x^2 + 32*x^3)*Log
[4])*Log[x] + (16*x^3 + 80*x^4 + 144*x^5 + 112*x^6 + 32*x^7)*Log[x]^2),x]

[Out]

Integrate[E^(100*x^2 - 40*x*Log[4] + 4*Log[4]^2 + 4*(-10*x^3 - 20*x^4 - 10*x^5 + (2*x^2 + 4*x^3 + 2*x^4)*Log[4
])*Log[x] + 4*(x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8)*Log[x]^2)*(200*x - 40*x^2 - 80*x^3 - 40*x^4 + (-40 + 8*x + 1
6*x^2 + 8*x^3)*Log[4] + (-120*x^2 - 312*x^3 - 168*x^4 + 48*x^5 + 32*x^6 + 8*x^7 + (16*x + 48*x^2 + 32*x^3)*Log
[4])*Log[x] + (16*x^3 + 80*x^4 + 144*x^5 + 112*x^6 + 32*x^7)*Log[x]^2), x]

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fricas [B]  time = 0.65, size = 82, normalized size = 3.73 \begin {gather*} e^{\left (4 \, {\left (x^{8} + 4 \, x^{7} + 6 \, x^{6} + 4 \, x^{5} + x^{4}\right )} \log \relax (x)^{2} + 100 \, x^{2} - 80 \, x \log \relax (2) + 16 \, \log \relax (2)^{2} - 8 \, {\left (5 \, x^{5} + 10 \, x^{4} + 5 \, x^{3} - 2 \, {\left (x^{4} + 2 \, x^{3} + x^{2}\right )} \log \relax (2)\right )} \log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^7+112*x^6+144*x^5+80*x^4+16*x^3)*log(x)^2+(2*(32*x^3+48*x^2+16*x)*log(2)+8*x^7+32*x^6+48*x^5-
168*x^4-312*x^3-120*x^2)*log(x)+2*(8*x^3+16*x^2+8*x-40)*log(2)-40*x^4-80*x^3-40*x^2+200*x)*exp((x^8+4*x^7+6*x^
6+4*x^5+x^4)*log(x)^2+(2*(2*x^4+4*x^3+2*x^2)*log(2)-10*x^5-20*x^4-10*x^3)*log(x)+4*log(2)^2-20*x*log(2)+25*x^2
)^4,x, algorithm="fricas")

[Out]

e^(4*(x^8 + 4*x^7 + 6*x^6 + 4*x^5 + x^4)*log(x)^2 + 100*x^2 - 80*x*log(2) + 16*log(2)^2 - 8*(5*x^5 + 10*x^4 +
5*x^3 - 2*(x^4 + 2*x^3 + x^2)*log(2))*log(x))

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giac [B]  time = 0.37, size = 111, normalized size = 5.05 \begin {gather*} e^{\left (4 \, x^{8} \log \relax (x)^{2} + 16 \, x^{7} \log \relax (x)^{2} + 24 \, x^{6} \log \relax (x)^{2} + 16 \, x^{5} \log \relax (x)^{2} - 40 \, x^{5} \log \relax (x) + 16 \, x^{4} \log \relax (2) \log \relax (x) + 4 \, x^{4} \log \relax (x)^{2} - 80 \, x^{4} \log \relax (x) + 32 \, x^{3} \log \relax (2) \log \relax (x) - 40 \, x^{3} \log \relax (x) + 16 \, x^{2} \log \relax (2) \log \relax (x) + 100 \, x^{2} - 80 \, x \log \relax (2) + 16 \, \log \relax (2)^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^7+112*x^6+144*x^5+80*x^4+16*x^3)*log(x)^2+(2*(32*x^3+48*x^2+16*x)*log(2)+8*x^7+32*x^6+48*x^5-
168*x^4-312*x^3-120*x^2)*log(x)+2*(8*x^3+16*x^2+8*x-40)*log(2)-40*x^4-80*x^3-40*x^2+200*x)*exp((x^8+4*x^7+6*x^
6+4*x^5+x^4)*log(x)^2+(2*(2*x^4+4*x^3+2*x^2)*log(2)-10*x^5-20*x^4-10*x^3)*log(x)+4*log(2)^2-20*x*log(2)+25*x^2
)^4,x, algorithm="giac")

[Out]

e^(4*x^8*log(x)^2 + 16*x^7*log(x)^2 + 24*x^6*log(x)^2 + 16*x^5*log(x)^2 - 40*x^5*log(x) + 16*x^4*log(2)*log(x)
+ 4*x^4*log(x)^2 - 80*x^4*log(x) + 32*x^3*log(2)*log(x) - 40*x^3*log(x) + 16*x^2*log(2)*log(x) + 100*x^2 - 80
*x*log(2) + 16*log(2)^2)

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maple [B]  time = 0.05, size = 87, normalized size = 3.95

method	result	size
risch	\(1048576^{-4 x} x^{8 x^{2} \left (x +1\right )^{2} \left (2 \ln \relax (2)-5 x \right )} {\mathrm e}^{4 x^{8} \ln \relax (x )^{2}+16 x^{7} \ln \relax (x )^{2}+24 x^{6} \ln \relax (x )^{2}+16 x^{5} \ln \relax (x )^{2}+4 x^{4} \ln \relax (x )^{2}+16 \ln \relax (2)^{2}+100 x^{2}}\)	\(87\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((32*x^7+112*x^6+144*x^5+80*x^4+16*x^3)*ln(x)^2+(2*(32*x^3+48*x^2+16*x)*ln(2)+8*x^7+32*x^6+48*x^5-168*x^4-
312*x^3-120*x^2)*ln(x)+2*(8*x^3+16*x^2+8*x-40)*ln(2)-40*x^4-80*x^3-40*x^2+200*x)*exp((x^8+4*x^7+6*x^6+4*x^5+x^
4)*ln(x)^2+(2*(2*x^4+4*x^3+2*x^2)*ln(2)-10*x^5-20*x^4-10*x^3)*ln(x)+4*ln(2)^2-20*x*ln(2)+25*x^2)^4,x,method=_R
ETURNVERBOSE)

[Out]

((1/1048576)^x)^4*(x^(2*x^2*(x+1)^2*(2*ln(2)-5*x)))^4*exp(4*x^8*ln(x)^2+16*x^7*ln(x)^2+24*x^6*ln(x)^2+16*x^5*l
n(x)^2+4*x^4*ln(x)^2+16*ln(2)^2+100*x^2)

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maxima [B]  time = 0.76, size = 111, normalized size = 5.05 \begin {gather*} e^{\left (4 \, x^{8} \log \relax (x)^{2} + 16 \, x^{7} \log \relax (x)^{2} + 24 \, x^{6} \log \relax (x)^{2} + 16 \, x^{5} \log \relax (x)^{2} - 40 \, x^{5} \log \relax (x) + 16 \, x^{4} \log \relax (2) \log \relax (x) + 4 \, x^{4} \log \relax (x)^{2} - 80 \, x^{4} \log \relax (x) + 32 \, x^{3} \log \relax (2) \log \relax (x) - 40 \, x^{3} \log \relax (x) + 16 \, x^{2} \log \relax (2) \log \relax (x) + 100 \, x^{2} - 80 \, x \log \relax (2) + 16 \, \log \relax (2)^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^7+112*x^6+144*x^5+80*x^4+16*x^3)*log(x)^2+(2*(32*x^3+48*x^2+16*x)*log(2)+8*x^7+32*x^6+48*x^5-
168*x^4-312*x^3-120*x^2)*log(x)+2*(8*x^3+16*x^2+8*x-40)*log(2)-40*x^4-80*x^3-40*x^2+200*x)*exp((x^8+4*x^7+6*x^
6+4*x^5+x^4)*log(x)^2+(2*(2*x^4+4*x^3+2*x^2)*log(2)-10*x^5-20*x^4-10*x^3)*log(x)+4*log(2)^2-20*x*log(2)+25*x^2
)^4,x, algorithm="maxima")

[Out]

e^(4*x^8*log(x)^2 + 16*x^7*log(x)^2 + 24*x^6*log(x)^2 + 16*x^5*log(x)^2 - 40*x^5*log(x) + 16*x^4*log(2)*log(x)
+ 4*x^4*log(x)^2 - 80*x^4*log(x) + 32*x^3*log(2)*log(x) - 40*x^3*log(x) + 16*x^2*log(2)*log(x) + 100*x^2 - 80
*x*log(2) + 16*log(2)^2)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int {\mathrm {e}}^{4\,{\ln \relax (x)}^2\,\left (x^8+4\,x^7+6\,x^6+4\,x^5+x^4\right )-80\,x\,\ln \relax (2)-4\,\ln \relax (x)\,\left (10\,x^3-2\,\ln \relax (2)\,\left (2\,x^4+4\,x^3+2\,x^2\right )+20\,x^4+10\,x^5\right )+16\,{\ln \relax (2)}^2+100\,x^2}\,\left (200\,x+{\ln \relax (x)}^2\,\left (32\,x^7+112\,x^6+144\,x^5+80\,x^4+16\,x^3\right )+\ln \relax (x)\,\left (2\,\ln \relax (2)\,\left (32\,x^3+48\,x^2+16\,x\right )-120\,x^2-312\,x^3-168\,x^4+48\,x^5+32\,x^6+8\,x^7\right )+2\,\ln \relax (2)\,\left (8\,x^3+16\,x^2+8\,x-40\right )-40\,x^2-80\,x^3-40\,x^4\right ) \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(4*log(x)^2*(x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8) - 80*x*log(2) - 4*log(x)*(10*x^3 - 2*log(2)*(2*x^2 + 4*
x^3 + 2*x^4) + 20*x^4 + 10*x^5) + 16*log(2)^2 + 100*x^2)*(200*x + log(x)^2*(16*x^3 + 80*x^4 + 144*x^5 + 112*x^
6 + 32*x^7) + log(x)*(2*log(2)*(16*x + 48*x^2 + 32*x^3) - 120*x^2 - 312*x^3 - 168*x^4 + 48*x^5 + 32*x^6 + 8*x^
7) + 2*log(2)*(8*x + 16*x^2 + 8*x^3 - 40) - 40*x^2 - 80*x^3 - 40*x^4),x)

[Out]

int(exp(4*log(x)^2*(x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8) - 80*x*log(2) - 4*log(x)*(10*x^3 - 2*log(2)*(2*x^2 + 4*
x^3 + 2*x^4) + 20*x^4 + 10*x^5) + 16*log(2)^2 + 100*x^2)*(200*x + log(x)^2*(16*x^3 + 80*x^4 + 144*x^5 + 112*x^
6 + 32*x^7) + log(x)*(2*log(2)*(16*x + 48*x^2 + 32*x^3) - 120*x^2 - 312*x^3 - 168*x^4 + 48*x^5 + 32*x^6 + 8*x^
7) + 2*log(2)*(8*x + 16*x^2 + 8*x^3 - 40) - 40*x^2 - 80*x^3 - 40*x^4), x)

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sympy [B]  time = 0.84, size = 87, normalized size = 3.95 \begin {gather*} e^{100 x^{2} - 80 x \log {\relax (2 )} + 4 \left (- 10 x^{5} - 20 x^{4} - 10 x^{3} + \left (4 x^{4} + 8 x^{3} + 4 x^{2}\right ) \log {\relax (2 )}\right ) \log {\relax (x )} + 4 \left (x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + x^{4}\right ) \log {\relax (x )}^{2} + 16 \log {\relax (2 )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x**7+112*x**6+144*x**5+80*x**4+16*x**3)*ln(x)**2+(2*(32*x**3+48*x**2+16*x)*ln(2)+8*x**7+32*x**6
+48*x**5-168*x**4-312*x**3-120*x**2)*ln(x)+2*(8*x**3+16*x**2+8*x-40)*ln(2)-40*x**4-80*x**3-40*x**2+200*x)*exp(
(x**8+4*x**7+6*x**6+4*x**5+x**4)*ln(x)**2+(2*(2*x**4+4*x**3+2*x**2)*ln(2)-10*x**5-20*x**4-10*x**3)*ln(x)+4*ln(
2)**2-20*x*ln(2)+25*x**2)**4,x)

[Out]

exp(100*x**2 - 80*x*log(2) + 4*(-10*x**5 - 20*x**4 - 10*x**3 + (4*x**4 + 8*x**3 + 4*x**2)*log(2))*log(x) + 4*(
x**8 + 4*x**7 + 6*x**6 + 4*x**5 + x**4)*log(x)**2 + 16*log(2)**2)

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