Optimal. Leaf size=21 \[ e^{e^{2-\frac {6 \left (-10-\frac {e^x}{x}\right )}{x}}} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 1.13, 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 {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right ) \left (-60 x+e^x (-12+6 x)\right )}{x^3} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {6 \exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right ) (-2+x)}{x^3}-\frac {60 \exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2}\right ) \, dx\\ &=6 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right ) (-2+x)}{x^3} \, dx-60 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2} \, dx\\ &=6 \int \left (-\frac {2 \exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^3}+\frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2}\right ) \, dx-60 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2} \, dx\\ &=6 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2} \, dx-12 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^3} \, dx-60 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.17, size = 19, normalized size = 0.90 \begin {gather*} e^{e^{2+\frac {6 e^x}{x^2}+\frac {60}{x}}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.96, size = 19, normalized size = 0.90
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{\frac {6 \,{\mathrm e}^{x}+2 x^{2}+60 x}{x^{2}}}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.42, size = 16, normalized size = 0.76 \begin {gather*} e^{\left (e^{\left (\frac {60}{x} + \frac {6 \, e^{x}}{x^{2}} + 2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 56 vs.
\(2 (17) = 34\).
time = 0.44, size = 56, normalized size = 2.67 \begin {gather*} e^{\left (\frac {x^{2} e^{\left (\frac {2 \, {\left (x^{2} + 30 \, x + 3 \, e^{x}\right )}}{x^{2}}\right )} + 2 \, x^{2} + 60 \, x + 6 \, e^{x}}{x^{2}} - \frac {2 \, {\left (x^{2} + 30 \, x + 3 \, e^{x}\right )}}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.40, size = 19, normalized size = 0.90 \begin {gather*} e^{e^{\frac {4 \left (\frac {x^{2}}{2} + 15 x + \frac {3 e^{x}}{2}\right )}{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.35, size = 18, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^2\,{\mathrm {e}}^{\frac {6\,{\mathrm {e}}^x}{x^2}}\,{\mathrm {e}}^{60/x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________