3.55.48 \(\int \frac {e^{\frac {2+\frac {e^{30 x}}{19683}}{x}} (-2+\frac {e^{30 x} (-1+30 x)}{19683})}{x^2} \, dx\)

Optimal. Leaf size=24 \[ 4+e^{\frac {2+3 e^{10 (3 x-\log (3))}}{x}} \]

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Rubi [A]  time = 0.25, antiderivative size = 16, normalized size of antiderivative = 0.67, number of steps used = 1, number of rules used = 1, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {6706} \begin {gather*} e^{\frac {e^{30 x}+39366}{19683 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^((2 + E^(30*x)/19683)/x)*(-2 + (E^(30*x)*(-1 + 30*x))/19683))/x^2,x]

[Out]

E^((39366 + E^(30*x))/(19683*x))

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{\frac {39366+e^{30 x}}{19683 x}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.33, size = 16, normalized size = 0.67 \begin {gather*} e^{\frac {39366+e^{30 x}}{19683 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((2 + E^(30*x)/19683)/x)*(-2 + (E^(30*x)*(-1 + 30*x))/19683))/x^2,x]

[Out]

E^((39366 + E^(30*x))/(19683*x))

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fricas [A]  time = 0.57, size = 16, normalized size = 0.67 \begin {gather*} e^{\left (\frac {e^{\left (30 \, x - 9 \, \log \relax (3)\right )} + 2}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((30*x-1)*exp(-9*log(3)+30*x)-2)*exp((exp(-9*log(3)+30*x)+2)/x)/x^2,x, algorithm="fricas")

[Out]

e^((e^(30*x - 9*log(3)) + 2)/x)

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giac [A]  time = 0.15, size = 20, normalized size = 0.83 \begin {gather*} e^{\left (\frac {e^{\left (30 \, x - 9 \, \log \relax (3)\right )}}{x} + \frac {2}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((30*x-1)*exp(-9*log(3)+30*x)-2)*exp((exp(-9*log(3)+30*x)+2)/x)/x^2,x, algorithm="giac")

[Out]

e^(e^(30*x - 9*log(3))/x + 2/x)

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maple [A]  time = 0.19, size = 13, normalized size = 0.54

method	result	size
risch	\({\mathrm e}^{\frac {{\mathrm e}^{30 x}+39366}{19683 x}}\)	\(13\)
norman	\({\mathrm e}^{\frac {{\mathrm e}^{-9 \ln \relax (3)+30 x}+2}{x}}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((30*x-1)*exp(-9*ln(3)+30*x)-2)*exp((exp(-9*ln(3)+30*x)+2)/x)/x^2,x,method=_RETURNVERBOSE)

[Out]

exp(1/19683*(exp(30*x)+39366)/x)

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maxima [A]  time = 0.43, size = 16, normalized size = 0.67 \begin {gather*} e^{\left (\frac {e^{\left (30 \, x\right )}}{19683 \, x} + \frac {2}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((30*x-1)*exp(-9*log(3)+30*x)-2)*exp((exp(-9*log(3)+30*x)+2)/x)/x^2,x, algorithm="maxima")

[Out]

e^(1/19683*e^(30*x)/x + 2/x)

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mupad [B]  time = 3.45, size = 12, normalized size = 0.50 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{30\,x}+39366}{19683\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((exp(30*x - 9*log(3)) + 2)/x)*(exp(30*x - 9*log(3))*(30*x - 1) - 2))/x^2,x)

[Out]

exp((exp(30*x) + 39366)/(19683*x))

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sympy [A]  time = 0.18, size = 10, normalized size = 0.42 \begin {gather*} e^{\frac {\frac {e^{30 x}}{19683} + 2}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((30*x-1)*exp(-9*ln(3)+30*x)-2)*exp((exp(-9*ln(3)+30*x)+2)/x)/x**2,x)

[Out]

exp((exp(30*x)/19683 + 2)/x)

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