3.102.63 \(\int \frac {-500 x^3+500 x^3 \log (x)+(500 x-500 x^2) \log ^2(x)+(-500 x+750 x^2) \log ^3(x)+128000 e^{2 e^{256 x^2}+256 x^2} x \log ^5(x)+(-250+250 x) \log ^5(x)+e^{e^{256 x^2}} (-500 x \log ^2(x)+(500 x+128000 e^{256 x^2} x^3) \log ^3(x)+(250+e^{256 x^2} (-128000 x+128000 x^2)) \log ^5(x))}{\log ^5(x)} \, dx\)

Optimal. Leaf size=27 \[ 5 \left (5-5 \left (e^{e^{256 x^2}}+x+\frac {x^2}{\log ^2(x)}\right )\right )^2 \]

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Rubi [F]  time = 3.14, 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 {-500 x^3+500 x^3 \log (x)+\left (500 x-500 x^2\right ) \log ^2(x)+\left (-500 x+750 x^2\right ) \log ^3(x)+128000 e^{2 e^{256 x^2}+256 x^2} x \log ^5(x)+(-250+250 x) \log ^5(x)+e^{e^{256 x^2}} \left (-500 x \log ^2(x)+\left (500 x+128000 e^{256 x^2} x^3\right ) \log ^3(x)+\left (250+e^{256 x^2} \left (-128000 x+128000 x^2\right )\right ) \log ^5(x)\right )}{\log ^5(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-500*x^3 + 500*x^3*Log[x] + (500*x - 500*x^2)*Log[x]^2 + (-500*x + 750*x^2)*Log[x]^3 + 128000*E^(2*E^(256
*x^2) + 256*x^2)*x*Log[x]^5 + (-250 + 250*x)*Log[x]^5 + E^E^(256*x^2)*(-500*x*Log[x]^2 + (500*x + 128000*E^(25
6*x^2)*x^3)*Log[x]^3 + (250 + E^(256*x^2)*(-128000*x + 128000*x^2))*Log[x]^5))/Log[x]^5,x]

[Out]

-250*E^E^(256*x^2) + 125*E^(2*E^(256*x^2)) - 250*x + 125*x^2 + (125*x^4)/Log[x]^4 - (250*x^2)/Log[x]^2 + (250*
x^3)/Log[x]^2 + 250*Defer[Int][E^E^(256*x^2), x] + 128000*Defer[Int][E^(E^(256*x^2) + 256*x^2)*x^2, x] - 500*D
efer[Int][(E^E^(256*x^2)*x)/Log[x]^3, x] + 500*Defer[Int][(E^E^(256*x^2)*x)/Log[x]^2, x] + 128000*Defer[Int][(
E^(E^(256*x^2) + 256*x^2)*x^3)/Log[x]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {250 \left (x^2+\left (-1+e^{e^{256 x^2}}+x\right ) \log ^2(x)\right ) \left (-2 x+2 x \log (x)+\left (1+512 e^{e^{256 x^2}+256 x^2} x\right ) \log ^3(x)\right )}{\log ^5(x)} \, dx\\ &=250 \int \frac {\left (x^2+\left (-1+e^{e^{256 x^2}}+x\right ) \log ^2(x)\right ) \left (-2 x+2 x \log (x)+\left (1+512 e^{e^{256 x^2}+256 x^2} x\right ) \log ^3(x)\right )}{\log ^5(x)} \, dx\\ &=250 \int \left (\frac {512 e^{e^{256 x^2}+256 x^2} x \left (x^2-\log ^2(x)+e^{e^{256 x^2}} \log ^2(x)+x \log ^2(x)\right )}{\log ^2(x)}+\frac {\left (x^2-\log ^2(x)+e^{e^{256 x^2}} \log ^2(x)+x \log ^2(x)\right ) \left (-2 x+2 x \log (x)+\log ^3(x)\right )}{\log ^5(x)}\right ) \, dx\\ &=250 \int \frac {\left (x^2-\log ^2(x)+e^{e^{256 x^2}} \log ^2(x)+x \log ^2(x)\right ) \left (-2 x+2 x \log (x)+\log ^3(x)\right )}{\log ^5(x)} \, dx+128000 \int \frac {e^{e^{256 x^2}+256 x^2} x \left (x^2-\log ^2(x)+e^{e^{256 x^2}} \log ^2(x)+x \log ^2(x)\right )}{\log ^2(x)} \, dx\\ &=250 \int \frac {\left (x^2+\left (-1+e^{e^{256 x^2}}+x\right ) \log ^2(x)\right ) \left (-2 x+2 x \log (x)+\log ^3(x)\right )}{\log ^5(x)} \, dx+128000 \int \frac {e^{e^{256 x^2}+256 x^2} x \left (x^2+\left (-1+e^{e^{256 x^2}}+x\right ) \log ^2(x)\right )}{\log ^2(x)} \, dx\\ &=250 \int \left (\frac {e^{e^{256 x^2}} \left (-2 x+2 x \log (x)+\log ^3(x)\right )}{\log ^3(x)}+\frac {-2 x^3+2 x^3 \log (x)+2 x \log ^2(x)-2 x^2 \log ^2(x)-2 x \log ^3(x)+3 x^2 \log ^3(x)-\log ^5(x)+x \log ^5(x)}{\log ^5(x)}\right ) \, dx+128000 \int \left (e^{2 e^{256 x^2}+256 x^2} x+\frac {e^{e^{256 x^2}+256 x^2} x \left (x^2-\log ^2(x)+x \log ^2(x)\right )}{\log ^2(x)}\right ) \, dx\\ &=250 \int \frac {e^{e^{256 x^2}} \left (-2 x+2 x \log (x)+\log ^3(x)\right )}{\log ^3(x)} \, dx+250 \int \frac {-2 x^3+2 x^3 \log (x)+2 x \log ^2(x)-2 x^2 \log ^2(x)-2 x \log ^3(x)+3 x^2 \log ^3(x)-\log ^5(x)+x \log ^5(x)}{\log ^5(x)} \, dx+128000 \int e^{2 e^{256 x^2}+256 x^2} x \, dx+128000 \int \frac {e^{e^{256 x^2}+256 x^2} x \left (x^2-\log ^2(x)+x \log ^2(x)\right )}{\log ^2(x)} \, dx\\ &=250 \int \left (e^{e^{256 x^2}}-\frac {2 e^{e^{256 x^2}} x}{\log ^3(x)}+\frac {2 e^{e^{256 x^2}} x}{\log ^2(x)}\right ) \, dx+250 \int \left (-1+x-\frac {2 x^3}{\log ^5(x)}+\frac {2 x^3}{\log ^4(x)}-\frac {2 (-1+x) x}{\log ^3(x)}+\frac {x (-2+3 x)}{\log ^2(x)}\right ) \, dx+64000 \operatorname {Subst}\left (\int e^{2 e^{256 x}+256 x} \, dx,x,x^2\right )+128000 \int \left (e^{e^{256 x^2}+256 x^2} (-1+x) x+\frac {e^{e^{256 x^2}+256 x^2} x^3}{\log ^2(x)}\right ) \, dx\\ &=-250 x+125 x^2+250 \int e^{e^{256 x^2}} \, dx+250 \int \frac {x (-2+3 x)}{\log ^2(x)} \, dx+250 \operatorname {Subst}\left (\int e^{2 x} \, dx,x,e^{256 x^2}\right )-500 \int \frac {x^3}{\log ^5(x)} \, dx+500 \int \frac {x^3}{\log ^4(x)} \, dx-500 \int \frac {e^{e^{256 x^2}} x}{\log ^3(x)} \, dx-500 \int \frac {(-1+x) x}{\log ^3(x)} \, dx+500 \int \frac {e^{e^{256 x^2}} x}{\log ^2(x)} \, dx+128000 \int e^{e^{256 x^2}+256 x^2} (-1+x) x \, dx+128000 \int \frac {e^{e^{256 x^2}+256 x^2} x^3}{\log ^2(x)} \, dx\\ &=125 e^{2 e^{256 x^2}}-250 x+125 x^2+\frac {125 x^4}{\log ^4(x)}-\frac {500 x^4}{3 \log ^3(x)}+250 \int e^{e^{256 x^2}} \, dx+250 \int \left (-\frac {2 x}{\log ^2(x)}+\frac {3 x^2}{\log ^2(x)}\right ) \, dx-500 \int \left (-\frac {x}{\log ^3(x)}+\frac {x^2}{\log ^3(x)}\right ) \, dx-500 \int \frac {x^3}{\log ^4(x)} \, dx-500 \int \frac {e^{e^{256 x^2}} x}{\log ^3(x)} \, dx+500 \int \frac {e^{e^{256 x^2}} x}{\log ^2(x)} \, dx+\frac {2000}{3} \int \frac {x^3}{\log ^3(x)} \, dx+128000 \int \left (-e^{e^{256 x^2}+256 x^2} x+e^{e^{256 x^2}+256 x^2} x^2\right ) \, dx+128000 \int \frac {e^{e^{256 x^2}+256 x^2} x^3}{\log ^2(x)} \, dx\\ &=125 e^{2 e^{256 x^2}}-250 x+125 x^2+\frac {125 x^4}{\log ^4(x)}-\frac {1000 x^4}{3 \log ^2(x)}+250 \int e^{e^{256 x^2}} \, dx+500 \int \frac {x}{\log ^3(x)} \, dx-500 \int \frac {e^{e^{256 x^2}} x}{\log ^3(x)} \, dx-500 \int \frac {x^2}{\log ^3(x)} \, dx-500 \int \frac {x}{\log ^2(x)} \, dx+500 \int \frac {e^{e^{256 x^2}} x}{\log ^2(x)} \, dx-\frac {2000}{3} \int \frac {x^3}{\log ^3(x)} \, dx+750 \int \frac {x^2}{\log ^2(x)} \, dx+\frac {4000}{3} \int \frac {x^3}{\log ^2(x)} \, dx-128000 \int e^{e^{256 x^2}+256 x^2} x \, dx+128000 \int e^{e^{256 x^2}+256 x^2} x^2 \, dx+128000 \int \frac {e^{e^{256 x^2}+256 x^2} x^3}{\log ^2(x)} \, dx\\ &=125 e^{2 e^{256 x^2}}-250 x+125 x^2+\frac {125 x^4}{\log ^4(x)}-\frac {250 x^2}{\log ^2(x)}+\frac {250 x^3}{\log ^2(x)}+\frac {500 x^2}{\log (x)}-\frac {750 x^3}{\log (x)}-\frac {4000 x^4}{3 \log (x)}+250 \int e^{e^{256 x^2}} \, dx-500 \int \frac {e^{e^{256 x^2}} x}{\log ^3(x)} \, dx+500 \int \frac {x}{\log ^2(x)} \, dx+500 \int \frac {e^{e^{256 x^2}} x}{\log ^2(x)} \, dx-750 \int \frac {x^2}{\log ^2(x)} \, dx-1000 \int \frac {x}{\log (x)} \, dx-\frac {4000}{3} \int \frac {x^3}{\log ^2(x)} \, dx+2250 \int \frac {x^2}{\log (x)} \, dx+\frac {16000}{3} \int \frac {x^3}{\log (x)} \, dx-64000 \operatorname {Subst}\left (\int e^{e^{256 x}+256 x} \, dx,x,x^2\right )+128000 \int e^{e^{256 x^2}+256 x^2} x^2 \, dx+128000 \int \frac {e^{e^{256 x^2}+256 x^2} x^3}{\log ^2(x)} \, dx\\ &=125 e^{2 e^{256 x^2}}-250 x+125 x^2+\frac {125 x^4}{\log ^4(x)}-\frac {250 x^2}{\log ^2(x)}+\frac {250 x^3}{\log ^2(x)}+250 \int e^{e^{256 x^2}} \, dx-250 \operatorname {Subst}\left (\int e^x \, dx,x,e^{256 x^2}\right )-500 \int \frac {e^{e^{256 x^2}} x}{\log ^3(x)} \, dx+500 \int \frac {e^{e^{256 x^2}} x}{\log ^2(x)} \, dx+1000 \int \frac {x}{\log (x)} \, dx-1000 \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )-2250 \int \frac {x^2}{\log (x)} \, dx+2250 \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )-\frac {16000}{3} \int \frac {x^3}{\log (x)} \, dx+\frac {16000}{3} \operatorname {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )+128000 \int e^{e^{256 x^2}+256 x^2} x^2 \, dx+128000 \int \frac {e^{e^{256 x^2}+256 x^2} x^3}{\log ^2(x)} \, dx\\ &=-250 e^{e^{256 x^2}}+125 e^{2 e^{256 x^2}}-250 x+125 x^2-1000 \text {Ei}(2 \log (x))+2250 \text {Ei}(3 \log (x))+\frac {16000}{3} \text {Ei}(4 \log (x))+\frac {125 x^4}{\log ^4(x)}-\frac {250 x^2}{\log ^2(x)}+\frac {250 x^3}{\log ^2(x)}+250 \int e^{e^{256 x^2}} \, dx-500 \int \frac {e^{e^{256 x^2}} x}{\log ^3(x)} \, dx+500 \int \frac {e^{e^{256 x^2}} x}{\log ^2(x)} \, dx+1000 \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )-2250 \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )-\frac {16000}{3} \operatorname {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )+128000 \int e^{e^{256 x^2}+256 x^2} x^2 \, dx+128000 \int \frac {e^{e^{256 x^2}+256 x^2} x^3}{\log ^2(x)} \, dx\\ &=-250 e^{e^{256 x^2}}+125 e^{2 e^{256 x^2}}-250 x+125 x^2+\frac {125 x^4}{\log ^4(x)}-\frac {250 x^2}{\log ^2(x)}+\frac {250 x^3}{\log ^2(x)}+250 \int e^{e^{256 x^2}} \, dx-500 \int \frac {e^{e^{256 x^2}} x}{\log ^3(x)} \, dx+500 \int \frac {e^{e^{256 x^2}} x}{\log ^2(x)} \, dx+128000 \int e^{e^{256 x^2}+256 x^2} x^2 \, dx+128000 \int \frac {e^{e^{256 x^2}+256 x^2} x^3}{\log ^2(x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.75, size = 62, normalized size = 2.30 \begin {gather*} 125 \left (e^{2 e^{256 x^2}}+2 e^{e^{256 x^2}} (-1+x)+(-2+x) x+\frac {x^4}{\log ^4(x)}+\frac {2 x^2 \left (-1+e^{e^{256 x^2}}+x\right )}{\log ^2(x)}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-500*x^3 + 500*x^3*Log[x] + (500*x - 500*x^2)*Log[x]^2 + (-500*x + 750*x^2)*Log[x]^3 + 128000*E^(2*
E^(256*x^2) + 256*x^2)*x*Log[x]^5 + (-250 + 250*x)*Log[x]^5 + E^E^(256*x^2)*(-500*x*Log[x]^2 + (500*x + 128000
*E^(256*x^2)*x^3)*Log[x]^3 + (250 + E^(256*x^2)*(-128000*x + 128000*x^2))*Log[x]^5))/Log[x]^5,x]

[Out]

125*(E^(2*E^(256*x^2)) + 2*E^E^(256*x^2)*(-1 + x) + (-2 + x)*x + x^4/Log[x]^4 + (2*x^2*(-1 + E^E^(256*x^2) + x
))/Log[x]^2)

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fricas [B]  time = 1.08, size = 77, normalized size = 2.85 \begin {gather*} \frac {125 \, {\left ({\left (x^{2} - 2 \, x\right )} \log \relax (x)^{4} + e^{\left (2 \, e^{\left (256 \, x^{2}\right )}\right )} \log \relax (x)^{4} + x^{4} + 2 \, {\left (x^{3} - x^{2}\right )} \log \relax (x)^{2} + 2 \, {\left ({\left (x - 1\right )} \log \relax (x)^{4} + x^{2} \log \relax (x)^{2}\right )} e^{\left (e^{\left (256 \, x^{2}\right )}\right )}\right )}}{\log \relax (x)^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((128000*x*exp(256*x^2)*log(x)^5*exp(exp(256*x^2))^2+(((128000*x^2-128000*x)*exp(256*x^2)+250)*log(x)
^5+(128000*x^3*exp(256*x^2)+500*x)*log(x)^3-500*x*log(x)^2)*exp(exp(256*x^2))+(250*x-250)*log(x)^5+(750*x^2-50
0*x)*log(x)^3+(-500*x^2+500*x)*log(x)^2+500*x^3*log(x)-500*x^3)/log(x)^5,x, algorithm="fricas")

[Out]

125*((x^2 - 2*x)*log(x)^4 + e^(2*e^(256*x^2))*log(x)^4 + x^4 + 2*(x^3 - x^2)*log(x)^2 + 2*((x - 1)*log(x)^4 +
x^2*log(x)^2)*e^(e^(256*x^2)))/log(x)^4

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {250 \, {\left (512 \, x e^{\left (256 \, x^{2} + 2 \, e^{\left (256 \, x^{2}\right )}\right )} \log \relax (x)^{5} + {\left (x - 1\right )} \log \relax (x)^{5} + 2 \, x^{3} \log \relax (x) + {\left (3 \, x^{2} - 2 \, x\right )} \log \relax (x)^{3} - 2 \, x^{3} - 2 \, {\left (x^{2} - x\right )} \log \relax (x)^{2} + {\left ({\left (512 \, {\left (x^{2} - x\right )} e^{\left (256 \, x^{2}\right )} + 1\right )} \log \relax (x)^{5} + 2 \, {\left (256 \, x^{3} e^{\left (256 \, x^{2}\right )} + x\right )} \log \relax (x)^{3} - 2 \, x \log \relax (x)^{2}\right )} e^{\left (e^{\left (256 \, x^{2}\right )}\right )}\right )}}{\log \relax (x)^{5}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((128000*x*exp(256*x^2)*log(x)^5*exp(exp(256*x^2))^2+(((128000*x^2-128000*x)*exp(256*x^2)+250)*log(x)
^5+(128000*x^3*exp(256*x^2)+500*x)*log(x)^3-500*x*log(x)^2)*exp(exp(256*x^2))+(250*x-250)*log(x)^5+(750*x^2-50
0*x)*log(x)^3+(-500*x^2+500*x)*log(x)^2+500*x^3*log(x)-500*x^3)/log(x)^5,x, algorithm="giac")

[Out]

integrate(250*(512*x*e^(256*x^2 + 2*e^(256*x^2))*log(x)^5 + (x - 1)*log(x)^5 + 2*x^3*log(x) + (3*x^2 - 2*x)*lo
g(x)^3 - 2*x^3 - 2*(x^2 - x)*log(x)^2 + ((512*(x^2 - x)*e^(256*x^2) + 1)*log(x)^5 + 2*(256*x^3*e^(256*x^2) + x
)*log(x)^3 - 2*x*log(x)^2)*e^(e^(256*x^2)))/log(x)^5, x)

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maple [B]  time = 0.18, size = 76, normalized size = 2.81

method	result	size
risch	\(125 x^{2}-250 x +\frac {125 x^{2} \left (2 x \ln \relax (x )^{2}+x^{2}-2 \ln \relax (x )^{2}\right )}{\ln \relax (x )^{4}}+125 \,{\mathrm e}^{2 \,{\mathrm e}^{256 x^{2}}}+\frac {250 \left (x \ln \relax (x )^{2}+x^{2}-\ln \relax (x )^{2}\right ) {\mathrm e}^{{\mathrm e}^{256 x^{2}}}}{\ln \relax (x )^{2}}\)	\(76\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((128000*x*exp(256*x^2)*ln(x)^5*exp(exp(256*x^2))^2+(((128000*x^2-128000*x)*exp(256*x^2)+250)*ln(x)^5+(1280
00*x^3*exp(256*x^2)+500*x)*ln(x)^3-500*x*ln(x)^2)*exp(exp(256*x^2))+(250*x-250)*ln(x)^5+(750*x^2-500*x)*ln(x)^
3+(-500*x^2+500*x)*ln(x)^2+500*x^3*ln(x)-500*x^3)/ln(x)^5,x,method=_RETURNVERBOSE)

[Out]

125*x^2-250*x+125*x^2*(2*x*ln(x)^2+x^2-2*ln(x)^2)/ln(x)^4+125*exp(2*exp(256*x^2))+250*(x*ln(x)^2+x^2-ln(x)^2)/
ln(x)^2*exp(exp(256*x^2))

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maxima [B]  time = 0.39, size = 74, normalized size = 2.74 \begin {gather*} 125 \, x^{2} - 250 \, x + \frac {125 \, {\left (e^{\left (2 \, e^{\left (256 \, x^{2}\right )}\right )} \log \relax (x)^{4} + x^{4} + 2 \, {\left (x^{3} - x^{2}\right )} \log \relax (x)^{2} + 2 \, {\left ({\left (x - 1\right )} \log \relax (x)^{4} + x^{2} \log \relax (x)^{2}\right )} e^{\left (e^{\left (256 \, x^{2}\right )}\right )}\right )}}{\log \relax (x)^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((128000*x*exp(256*x^2)*log(x)^5*exp(exp(256*x^2))^2+(((128000*x^2-128000*x)*exp(256*x^2)+250)*log(x)
^5+(128000*x^3*exp(256*x^2)+500*x)*log(x)^3-500*x*log(x)^2)*exp(exp(256*x^2))+(250*x-250)*log(x)^5+(750*x^2-50
0*x)*log(x)^3+(-500*x^2+500*x)*log(x)^2+500*x^3*log(x)-500*x^3)/log(x)^5,x, algorithm="maxima")

[Out]

125*x^2 - 250*x + 125*(e^(2*e^(256*x^2))*log(x)^4 + x^4 + 2*(x^3 - x^2)*log(x)^2 + 2*((x - 1)*log(x)^4 + x^2*l
og(x)^2)*e^(e^(256*x^2)))/log(x)^4

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mupad [B]  time = 7.09, size = 82, normalized size = 3.04 \begin {gather*} 125\,{\mathrm {e}}^{2\,{\mathrm {e}}^{256\,x^2}}-250\,{\mathrm {e}}^{{\mathrm {e}}^{256\,x^2}}-250\,x-\frac {250\,x^2}{{\ln \relax (x)}^2}+\frac {250\,x^3}{{\ln \relax (x)}^2}+\frac {125\,x^4}{{\ln \relax (x)}^4}+125\,x^2+250\,x\,{\mathrm {e}}^{{\mathrm {e}}^{256\,x^2}}+\frac {250\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^{256\,x^2}}}{{\ln \relax (x)}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)^2*(500*x - 500*x^2) - log(x)^3*(500*x - 750*x^2) + 500*x^3*log(x) - 500*x^3 + log(x)^5*(250*x - 25
0) - exp(exp(256*x^2))*(500*x*log(x)^2 + log(x)^5*(exp(256*x^2)*(128000*x - 128000*x^2) - 250) - log(x)^3*(500
*x + 128000*x^3*exp(256*x^2))) + 128000*x*exp(2*exp(256*x^2))*exp(256*x^2)*log(x)^5)/log(x)^5,x)

[Out]

125*exp(2*exp(256*x^2)) - 250*exp(exp(256*x^2)) - 250*x - (250*x^2)/log(x)^2 + (250*x^3)/log(x)^2 + (125*x^4)/
log(x)^4 + 125*x^2 + 250*x*exp(exp(256*x^2)) + (250*x^2*exp(exp(256*x^2)))/log(x)^2

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sympy [B]  time = 0.45, size = 83, normalized size = 3.07 \begin {gather*} 125 x^{2} - 250 x + \frac {125 x^{4} + \left (250 x^{3} - 250 x^{2}\right ) \log {\relax (x )}^{2}}{\log {\relax (x )}^{4}} + \frac {\left (250 x^{2} + 250 x \log {\relax (x )}^{2} - 250 \log {\relax (x )}^{2}\right ) e^{e^{256 x^{2}}} + 125 e^{2 e^{256 x^{2}}} \log {\relax (x )}^{2}}{\log {\relax (x )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((128000*x*exp(256*x**2)*ln(x)**5*exp(exp(256*x**2))**2+(((128000*x**2-128000*x)*exp(256*x**2)+250)*l
n(x)**5+(128000*x**3*exp(256*x**2)+500*x)*ln(x)**3-500*x*ln(x)**2)*exp(exp(256*x**2))+(250*x-250)*ln(x)**5+(75
0*x**2-500*x)*ln(x)**3+(-500*x**2+500*x)*ln(x)**2+500*x**3*ln(x)-500*x**3)/ln(x)**5,x)

[Out]

125*x**2 - 250*x + (125*x**4 + (250*x**3 - 250*x**2)*log(x)**2)/log(x)**4 + ((250*x**2 + 250*x*log(x)**2 - 250
*log(x)**2)*exp(exp(256*x**2)) + 125*exp(2*exp(256*x**2))*log(x)**2)/log(x)**2

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