∫ 18055103407718400−268738560x log4(x)+x2 log8(x)+e− e5+x log4(x)______ −134369280+x log4(x) (537477120e5+x log3(x)+134369280e5+xx log4(x)+e5+x(x−x2) log8(x)) ___________________________________________________________________________________________________________________________________________________________________________________________________18055103407718400x−268738560x2 log4(x)+x3 log8(x) dx

3.27.23 \(\int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} (x-x^2) \log ^8(x))}{18055103407718400 x-268738560 x^2 \log ^4(x)+x^3 \log ^8(x)} \, dx\)

Optimal. Leaf size=23 \[ e^{\frac {e^{5+x}}{-x+\frac {134369280}{\log ^4(x)}}}+\log (x) \]

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Rubi [F] time = 16.58, 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 {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{18055103407718400 x-268738560 x^2 \log ^4(x)+x^3 \log ^8(x)} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(18055103407718400 - 268738560*x*Log[x]^4 + x^2*Log[x]^8 + (537477120*E^(5 + x)*Log[x]^3 + 134369280*E^(5

+ x)*x*Log[x]^4 + E^(5 + x)*(x - x^2)*Log[x]^8)/E^((E^(5 + x)*Log[x]^4)/(-134369280 + x*Log[x]^4)))/(180551034

07718400*x - 268738560*x^2*Log[x]^4 + x^3*Log[x]^8),x]

[Out]

Log[x] + Defer[Int][E^(5 + x + (E^(5 + x)*Log[x]^4)/(134369280 - x*Log[x]^4))/x^2, x] - Defer[Int][E^(5 + x +

(E^(5 + x)*Log[x]^4)/(134369280 - x*Log[x]^4))/x, x] + 18055103407718400*Defer[Int][E^(5 + x + (E^(5 + x)*Log[

x]^4)/(134369280 - x*Log[x]^4))/(x^2*(-134369280 + x*Log[x]^4)^2), x] + 537477120*Defer[Int][(E^(5 + x + (E^(5

+ x)*Log[x]^4)/(134369280 - x*Log[x]^4))*Log[x]^3)/(x*(-134369280 + x*Log[x]^4)^2), x] + 268738560*Defer[Int]

[E^(5 + x + (E^(5 + x)*Log[x]^4)/(134369280 - x*Log[x]^4))/(x^2*(-134369280 + x*Log[x]^4)), x] - 134369280*Def

er[Int][E^(5 + x + (E^(5 + x)*Log[x]^4)/(134369280 - x*Log[x]^4))/(x*(-134369280 + x*Log[x]^4)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{x \left (134369280-x \log ^4(x)\right )^2} \, dx\\ &=\int \left (\frac {1}{x}-\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \log ^3(x) \left (-537477120-134369280 x \log (x)-x \log ^5(x)+x^2 \log ^5(x)\right )}{x \left (-134369280+x \log ^4(x)\right )^2}\right ) \, dx\\ &=\log (x)-\int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \log ^3(x) \left (-537477120-134369280 x \log (x)-x \log ^5(x)+x^2 \log ^5(x)\right )}{x \left (-134369280+x \log ^4(x)\right )^2} \, dx\\ &=\log (x)-\int \left (\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} (-1+x)}{x^2}-\frac {537477120 e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \left (33592320+x \log ^3(x)\right )}{x^2 \left (-134369280+x \log ^4(x)\right )^2}+\frac {134369280 e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} (-2+x)}{x^2 \left (-134369280+x \log ^4(x)\right )}\right ) \, dx\\ &=\log (x)-134369280 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} (-2+x)}{x^2 \left (-134369280+x \log ^4(x)\right )} \, dx+537477120 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \left (33592320+x \log ^3(x)\right )}{x^2 \left (-134369280+x \log ^4(x)\right )^2} \, dx-\int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} (-1+x)}{x^2} \, dx\\ &=\log (x)-134369280 \int \left (-\frac {2 e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2 \left (-134369280+x \log ^4(x)\right )}+\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x \left (-134369280+x \log ^4(x)\right )}\right ) \, dx+537477120 \int \left (\frac {33592320 e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2 \left (-134369280+x \log ^4(x)\right )^2}+\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \log ^3(x)}{x \left (-134369280+x \log ^4(x)\right )^2}\right ) \, dx-\int \left (-\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2}+\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x}\right ) \, dx\\ &=\log (x)-134369280 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x \left (-134369280+x \log ^4(x)\right )} \, dx+268738560 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2 \left (-134369280+x \log ^4(x)\right )} \, dx+537477120 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \log ^3(x)}{x \left (-134369280+x \log ^4(x)\right )^2} \, dx+18055103407718400 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2 \left (-134369280+x \log ^4(x)\right )^2} \, dx+\int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2} \, dx-\int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 3.19, size = 26, normalized size = 1.13 \begin {gather*} e^{\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}+\log (x) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(18055103407718400 - 268738560*x*Log[x]^4 + x^2*Log[x]^8 + (537477120*E^(5 + x)*Log[x]^3 + 134369280

*E^(5 + x)*x*Log[x]^4 + E^(5 + x)*(x - x^2)*Log[x]^8)/E^((E^(5 + x)*Log[x]^4)/(-134369280 + x*Log[x]^4)))/(180

55103407718400*x - 268738560*x^2*Log[x]^4 + x^3*Log[x]^8),x]

[Out]

E^((E^(5 + x)*Log[x]^4)/(134369280 - x*Log[x]^4)) + Log[x]

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fricas [A] time = 0.62, size = 24, normalized size = 1.04 \begin {gather*} e^{\left (-\frac {e^{\left (x + 5\right )} \log \relax (x)^{4}}{x \log \relax (x)^{4} - 134369280}\right )} + \log \relax (x) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2+x)*exp(5+x)*log(x)^8+134369280*x*exp(5+x)*log(x)^4+537477120*exp(5+x)*log(x)^3)*exp(-exp(5+x

)*log(x)^4/(x*log(x)^4-134369280))+x^2*log(x)^8-268738560*x*log(x)^4+18055103407718400)/(x^3*log(x)^8-26873856

0*x^2*log(x)^4+18055103407718400*x),x, algorithm="fricas")

[Out]

e^(-e^(x + 5)*log(x)^4/(x*log(x)^4 - 134369280)) + log(x)

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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{2} \log \relax (x)^{8} - 268738560 \, x \log \relax (x)^{4} - {\left ({\left (x^{2} - x\right )} e^{\left (x + 5\right )} \log \relax (x)^{8} - 134369280 \, x e^{\left (x + 5\right )} \log \relax (x)^{4} - 537477120 \, e^{\left (x + 5\right )} \log \relax (x)^{3}\right )} e^{\left (-\frac {e^{\left (x + 5\right )} \log \relax (x)^{4}}{x \log \relax (x)^{4} - 134369280}\right )} + 18055103407718400}{x^{3} \log \relax (x)^{8} - 268738560 \, x^{2} \log \relax (x)^{4} + 18055103407718400 \, x}\,{d x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2+x)*exp(5+x)*log(x)^8+134369280*x*exp(5+x)*log(x)^4+537477120*exp(5+x)*log(x)^3)*exp(-exp(5+x

)*log(x)^4/(x*log(x)^4-134369280))+x^2*log(x)^8-268738560*x*log(x)^4+18055103407718400)/(x^3*log(x)^8-26873856

0*x^2*log(x)^4+18055103407718400*x),x, algorithm="giac")

[Out]

integrate((x^2*log(x)^8 - 268738560*x*log(x)^4 - ((x^2 - x)*e^(x + 5)*log(x)^8 - 134369280*x*e^(x + 5)*log(x)^

4 - 537477120*e^(x + 5)*log(x)^3)*e^(-e^(x + 5)*log(x)^4/(x*log(x)^4 - 134369280)) + 18055103407718400)/(x^3*l

og(x)^8 - 268738560*x^2*log(x)^4 + 18055103407718400*x), x)

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maple [A] time = 0.06, size = 25, normalized size = 1.09


method	result	size

risch	\(\ln \relax (x )+{\mathrm e}^{-\frac {{\mathrm e}^{5+x} \ln \relax (x )^{4}}{x \ln \relax (x )^{4}-134369280}}\)	\(25\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((((-x^2+x)*exp(5+x)*ln(x)^8+134369280*x*exp(5+x)*ln(x)^4+537477120*exp(5+x)*ln(x)^3)*exp(-exp(5+x)*ln(x)^4

/(x*ln(x)^4-134369280))+x^2*ln(x)^8-268738560*x*ln(x)^4+18055103407718400)/(x^3*ln(x)^8-268738560*x^2*ln(x)^4+

18055103407718400*x),x,method=_RETURNVERBOSE)

[Out]

ln(x)+exp(-exp(5+x)*ln(x)^4/(x*ln(x)^4-134369280))

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maxima [A] time = 0.53, size = 24, normalized size = 1.04 \begin {gather*} e^{\left (-\frac {e^{\left (x + 5\right )} \log \relax (x)^{4}}{x \log \relax (x)^{4} - 134369280}\right )} + \log \relax (x) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2+x)*exp(5+x)*log(x)^8+134369280*x*exp(5+x)*log(x)^4+537477120*exp(5+x)*log(x)^3)*exp(-exp(5+x

)*log(x)^4/(x*log(x)^4-134369280))+x^2*log(x)^8-268738560*x*log(x)^4+18055103407718400)/(x^3*log(x)^8-26873856

0*x^2*log(x)^4+18055103407718400*x),x, algorithm="maxima")

[Out]

e^(-e^(x + 5)*log(x)^4/(x*log(x)^4 - 134369280)) + log(x)

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mupad [B] time = 1.71, size = 24, normalized size = 1.04 \begin {gather*} {\mathrm {e}}^{-\frac {{\mathrm {e}}^5\,{\mathrm {e}}^x\,{\ln \relax (x)}^4}{x\,{\ln \relax (x)}^4-134369280}}+\ln \relax (x) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(exp(x + 5)*log(x)^4)/(x*log(x)^4 - 134369280))*(537477120*exp(x + 5)*log(x)^3 + 134369280*x*exp(x +

5)*log(x)^4 + exp(x + 5)*log(x)^8*(x - x^2)) - 268738560*x*log(x)^4 + x^2*log(x)^8 + 18055103407718400)/(1805

5103407718400*x - 268738560*x^2*log(x)^4 + x^3*log(x)^8),x)

[Out]

exp(-(exp(5)*exp(x)*log(x)^4)/(x*log(x)^4 - 134369280)) + log(x)

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sympy [A] time = 0.98, size = 24, normalized size = 1.04 \begin {gather*} \log {\relax (x )} + e^{- \frac {e^{x + 5} \log {\relax (x )}^{4}}{x \log {\relax (x )}^{4} - 134369280}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x**2+x)*exp(5+x)*ln(x)**8+134369280*x*exp(5+x)*ln(x)**4+537477120*exp(5+x)*ln(x)**3)*exp(-exp(5+

x)*ln(x)**4/(x*ln(x)**4-134369280))+x**2*ln(x)**8-268738560*x*ln(x)**4+18055103407718400)/(x**3*ln(x)**8-26873

8560*x**2*ln(x)**4+18055103407718400*x),x)

[Out]

log(x) + exp(-exp(x + 5)*log(x)**4/(x*log(x)**4 - 134369280))

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