3.52.30 \(\int \frac {x+x^{\frac {3 e^{e^3+4 x^2}}{x}} (3 e^{e^3+4 x^2}+e^{e^3+4 x^2} (-3+24 x^2) \log (x))}{x^2} \, dx\)

Optimal. Leaf size=21 \[ x^{\frac {3 e^{e^3+4 x^2}}{x}}+\log (x) \]

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Rubi [F]  time = 0.61, 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 {x+x^{\frac {3 e^{e^3+4 x^2}}{x}} \left (3 e^{e^3+4 x^2}+e^{e^3+4 x^2} \left (-3+24 x^2\right ) \log (x)\right )}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(x + x^((3*E^(E^3 + 4*x^2))/x)*(3*E^(E^3 + 4*x^2) + E^(E^3 + 4*x^2)*(-3 + 24*x^2)*Log[x]))/x^2,x]

[Out]

Log[x] + 3*Defer[Int][E^(E^3 + 4*x^2)*x^(-2 + (3*E^(E^3 + 4*x^2))/x), x] - 3*Log[x]*Defer[Int][E^(E^3 + 4*x^2)
*x^(-2 + (3*E^(E^3 + 4*x^2))/x), x] + 24*Log[x]*Defer[Int][E^(E^3 + 4*x^2)*x^((3*E^(E^3 + 4*x^2))/x), x] + 3*D
efer[Int][Defer[Int][E^(E^3 + 4*x^2)*x^(-2 + (3*E^(E^3 + 4*x^2))/x), x]/x, x] - 24*Defer[Int][Defer[Int][E^(E^
3 + 4*x^2)*x^((3*E^(E^3 + 4*x^2))/x), x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1}{x}+3 e^{e^3+4 x^2} x^{-2+\frac {3 e^{e^3+4 x^2}}{x}} \left (1-\log (x)+8 x^2 \log (x)\right )\right ) \, dx\\ &=\log (x)+3 \int e^{e^3+4 x^2} x^{-2+\frac {3 e^{e^3+4 x^2}}{x}} \left (1-\log (x)+8 x^2 \log (x)\right ) \, dx\\ &=\log (x)+3 \int \left (e^{e^3+4 x^2} x^{-2+\frac {3 e^{e^3+4 x^2}}{x}}-e^{e^3+4 x^2} x^{-2+\frac {3 e^{e^3+4 x^2}}{x}} \log (x)+8 e^{e^3+4 x^2} x^{\frac {3 e^{e^3+4 x^2}}{x}} \log (x)\right ) \, dx\\ &=\log (x)+3 \int e^{e^3+4 x^2} x^{-2+\frac {3 e^{e^3+4 x^2}}{x}} \, dx-3 \int e^{e^3+4 x^2} x^{-2+\frac {3 e^{e^3+4 x^2}}{x}} \log (x) \, dx+24 \int e^{e^3+4 x^2} x^{\frac {3 e^{e^3+4 x^2}}{x}} \log (x) \, dx\\ &=\log (x)+3 \int e^{e^3+4 x^2} x^{-2+\frac {3 e^{e^3+4 x^2}}{x}} \, dx+3 \int \frac {\int e^{e^3+4 x^2} x^{-2+\frac {3 e^{e^3+4 x^2}}{x}} \, dx}{x} \, dx-24 \int \frac {\int e^{e^3+4 x^2} x^{\frac {3 e^{e^3+4 x^2}}{x}} \, dx}{x} \, dx-(3 \log (x)) \int e^{e^3+4 x^2} x^{-2+\frac {3 e^{e^3+4 x^2}}{x}} \, dx+(24 \log (x)) \int e^{e^3+4 x^2} x^{\frac {3 e^{e^3+4 x^2}}{x}} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.32, size = 21, normalized size = 1.00 \begin {gather*} x^{\frac {3 e^{e^3+4 x^2}}{x}}+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(x + x^((3*E^(E^3 + 4*x^2))/x)*(3*E^(E^3 + 4*x^2) + E^(E^3 + 4*x^2)*(-3 + 24*x^2)*Log[x]))/x^2,x]

[Out]

x^((3*E^(E^3 + 4*x^2))/x) + Log[x]

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fricas [A]  time = 0.45, size = 19, normalized size = 0.90 \begin {gather*} x^{\frac {3 \, e^{\left (4 \, x^{2} + e^{3}\right )}}{x}} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x^2-3)*exp(exp(3)+4*x^2)*log(x)+3*exp(exp(3)+4*x^2))*exp(3*exp(exp(3)+4*x^2)*log(x)/x)+x)/x^2,
x, algorithm="fricas")

[Out]

x^(3*e^(4*x^2 + e^3)/x) + log(x)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {3 \, {\left ({\left (8 \, x^{2} - 1\right )} e^{\left (4 \, x^{2} + e^{3}\right )} \log \relax (x) + e^{\left (4 \, x^{2} + e^{3}\right )}\right )} x^{\frac {3 \, e^{\left (4 \, x^{2} + e^{3}\right )}}{x}} + x}{x^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x^2-3)*exp(exp(3)+4*x^2)*log(x)+3*exp(exp(3)+4*x^2))*exp(3*exp(exp(3)+4*x^2)*log(x)/x)+x)/x^2,
x, algorithm="giac")

[Out]

integrate((3*((8*x^2 - 1)*e^(4*x^2 + e^3)*log(x) + e^(4*x^2 + e^3))*x^(3*e^(4*x^2 + e^3)/x) + x)/x^2, x)

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maple [A]  time = 0.07, size = 20, normalized size = 0.95

method	result	size
risch	\(\ln \relax (x )+x^{\frac {3 \,{\mathrm e}^{{\mathrm e}^{3}+4 x^{2}}}{x}}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((24*x^2-3)*exp(exp(3)+4*x^2)*ln(x)+3*exp(exp(3)+4*x^2))*exp(3*exp(exp(3)+4*x^2)*ln(x)/x)+x)/x^2,x,method
=_RETURNVERBOSE)

[Out]

ln(x)+x^(3*exp(exp(3)+4*x^2)/x)

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maxima [A]  time = 0.59, size = 19, normalized size = 0.90 \begin {gather*} x^{\frac {3 \, e^{\left (4 \, x^{2} + e^{3}\right )}}{x}} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x^2-3)*exp(exp(3)+4*x^2)*log(x)+3*exp(exp(3)+4*x^2))*exp(3*exp(exp(3)+4*x^2)*log(x)/x)+x)/x^2,
x, algorithm="maxima")

[Out]

x^(3*e^(4*x^2 + e^3)/x) + log(x)

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mupad [B]  time = 3.35, size = 19, normalized size = 0.90 \begin {gather*} \ln \relax (x)+x^{\frac {3\,{\mathrm {e}}^{4\,x^2+{\mathrm {e}}^3}}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x + exp((3*exp(exp(3) + 4*x^2)*log(x))/x)*(3*exp(exp(3) + 4*x^2) + exp(exp(3) + 4*x^2)*log(x)*(24*x^2 - 3
)))/x^2,x)

[Out]

log(x) + x^((3*exp(exp(3) + 4*x^2))/x)

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sympy [A]  time = 0.45, size = 20, normalized size = 0.95 \begin {gather*} e^{\frac {3 e^{4 x^{2} + e^{3}} \log {\relax (x )}}{x}} + \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x**2-3)*exp(exp(3)+4*x**2)*ln(x)+3*exp(exp(3)+4*x**2))*exp(3*exp(exp(3)+4*x**2)*ln(x)/x)+x)/x*
*2,x)

[Out]

exp(3*exp(4*x**2 + exp(3))*log(x)/x) + log(x)

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