3.9.97 \(\int \frac {e^{e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}} (-18+x^4+5 x^5+10 x^5 \log (x))}{x^4} \, dx\)

Optimal. Leaf size=18 \[ e^{e^{\frac {6}{x^3}+x+5 x^2 \log (x)}} \]

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Rubi [F]  time = 2.99, 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 {\exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right ) \left (-18+x^4+5 x^5+10 x^5 \log (x)\right )}{x^4} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^((6 + x^4 + 5*x^5*Log[x])/x^3) + (6 + x^4 + 5*x^5*Log[x])/x^3)*(-18 + x^4 + 5*x^5 + 10*x^5*Log[x]))/
x^4,x]

[Out]

Defer[Int][E^(E^((6 + x^4 + 5*x^5*Log[x])/x^3) + (6 + x^4 + 5*x^5*Log[x])/x^3), x] - 18*Defer[Int][E^(E^((6 +
x^4 + 5*x^5*Log[x])/x^3) + (6 + x^4 + 5*x^5*Log[x])/x^3)/x^4, x] + 5*Defer[Int][E^(E^((6 + x^4 + 5*x^5*Log[x])
/x^3) + (6 + x^4 + 5*x^5*Log[x])/x^3)*x, x] + 10*Defer[Int][E^(E^((6 + x^4 + 5*x^5*Log[x])/x^3) + (6 + x^4 + 5
*x^5*Log[x])/x^3)*x*Log[x], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {\exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right ) \left (-18+x^4+5 x^5\right )}{x^4}+10 \exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right ) x \log (x)\right ) \, dx\\ &=10 \int \exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right ) x \log (x) \, dx+\int \frac {\exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right ) \left (-18+x^4+5 x^5\right )}{x^4} \, dx\\ &=10 \int \exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right ) x \log (x) \, dx+\int \left (\exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right )-\frac {18 \exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right )}{x^4}+5 \exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right ) x\right ) \, dx\\ &=5 \int \exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right ) x \, dx+10 \int \exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right ) x \log (x) \, dx-18 \int \frac {\exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right )}{x^4} \, dx+\int \exp \left (e^{\frac {6+x^4+5 x^5 \log (x)}{x^3}}+\frac {6+x^4+5 x^5 \log (x)}{x^3}\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.37, size = 19, normalized size = 1.06 \begin {gather*} e^{e^{\frac {6}{x^3}+x} x^{5 x^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^((6 + x^4 + 5*x^5*Log[x])/x^3) + (6 + x^4 + 5*x^5*Log[x])/x^3)*(-18 + x^4 + 5*x^5 + 10*x^5*Log
[x]))/x^4,x]

[Out]

E^(E^(6/x^3 + x)*x^(5*x^2))

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fricas [B]  time = 0.67, size = 56, normalized size = 3.11 \begin {gather*} e^{\left (\frac {5 \, x^{5} \log \relax (x) + x^{4} + x^{3} e^{\left (\frac {5 \, x^{5} \log \relax (x) + x^{4} + 6}{x^{3}}\right )} + 6}{x^{3}} - \frac {5 \, x^{5} \log \relax (x) + x^{4} + 6}{x^{3}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((10*x^5*log(x)+5*x^5+x^4-18)*exp((5*x^5*log(x)+x^4+6)/x^3)*exp(exp((5*x^5*log(x)+x^4+6)/x^3))/x^4,x,
algorithm="fricas")

[Out]

e^((5*x^5*log(x) + x^4 + x^3*e^((5*x^5*log(x) + x^4 + 6)/x^3) + 6)/x^3 - (5*x^5*log(x) + x^4 + 6)/x^3)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (10 \, x^{5} \log \relax (x) + 5 \, x^{5} + x^{4} - 18\right )} e^{\left (\frac {5 \, x^{5} \log \relax (x) + x^{4} + 6}{x^{3}} + e^{\left (\frac {5 \, x^{5} \log \relax (x) + x^{4} + 6}{x^{3}}\right )}\right )}}{x^{4}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((10*x^5*log(x)+5*x^5+x^4-18)*exp((5*x^5*log(x)+x^4+6)/x^3)*exp(exp((5*x^5*log(x)+x^4+6)/x^3))/x^4,x,
algorithm="giac")

[Out]

integrate((10*x^5*log(x) + 5*x^5 + x^4 - 18)*e^((5*x^5*log(x) + x^4 + 6)/x^3 + e^((5*x^5*log(x) + x^4 + 6)/x^3
))/x^4, x)

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maple [A]  time = 0.02, size = 19, normalized size = 1.06

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{\frac {5 x^{5} \ln \relax (x )+x^{4}+6}{x^{3}}}}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*x^5*ln(x)+5*x^5+x^4-18)*exp((5*x^5*ln(x)+x^4+6)/x^3)*exp(exp((5*x^5*ln(x)+x^4+6)/x^3))/x^4,x,method=_R
ETURNVERBOSE)

[Out]

exp(exp((5*x^5*ln(x)+x^4+6)/x^3))

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maxima [A]  time = 0.84, size = 16, normalized size = 0.89 \begin {gather*} e^{\left (e^{\left (5 \, x^{2} \log \relax (x) + x + \frac {6}{x^{3}}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((10*x^5*log(x)+5*x^5+x^4-18)*exp((5*x^5*log(x)+x^4+6)/x^3)*exp(exp((5*x^5*log(x)+x^4+6)/x^3))/x^4,x,
algorithm="maxima")

[Out]

e^(e^(5*x^2*log(x) + x + 6/x^3))

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mupad [B]  time = 0.74, size = 17, normalized size = 0.94 \begin {gather*} {\mathrm {e}}^{x^{5\,x^2}\,{\mathrm {e}}^{x+\frac {6}{x^3}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp((5*x^5*log(x) + x^4 + 6)/x^3))*exp((5*x^5*log(x) + x^4 + 6)/x^3)*(10*x^5*log(x) + x^4 + 5*x^5 - 1
8))/x^4,x)

[Out]

exp(x^(5*x^2)*exp(x + 6/x^3))

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sympy [A]  time = 1.13, size = 19, normalized size = 1.06 \begin {gather*} e^{e^{\frac {5 x^{5} \log {\relax (x )} + x^{4} + 6}{x^{3}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((10*x**5*ln(x)+5*x**5+x**4-18)*exp((5*x**5*ln(x)+x**4+6)/x**3)*exp(exp((5*x**5*ln(x)+x**4+6)/x**3))/
x**4,x)

[Out]

exp(exp((5*x**5*log(x) + x**4 + 6)/x**3))

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