Optimal. Leaf size=21 \[ -2+e^{e^{\frac {e^{x^2}}{x}}} (5+x)^2 \]
[Out]
________________________________________________________________________________________
Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(62\) vs. \(2(21)=42\).
time = 0.18, antiderivative size = 62, normalized size of antiderivative = 2.95, number of steps
used = 1, number of rules used = 1, integrand size = 64, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {2326}
\begin {gather*} -\frac {e^{x^2+e^{\frac {e^{x^2}}{x}}} \left (-2 x^4-20 x^3-49 x^2+10 x+25\right )}{\left (2 e^{x^2}-\frac {e^{x^2}}{x^2}\right ) x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {e^{e^{\frac {e^{x^2}}{x}}+x^2} \left (25+10 x-49 x^2-20 x^3-2 x^4\right )}{\left (2 e^{x^2}-\frac {e^{x^2}}{x^2}\right ) x^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.08, size = 19, normalized size = 0.90 \begin {gather*} e^{e^{\frac {e^{x^2}}{x}}} (5+x)^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.18, size = 20, normalized size = 0.95
method | result | size |
risch | \(\left (x^{2}+10 x +25\right ) {\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{x^{2}}}{x}}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.31, size = 19, normalized size = 0.90 \begin {gather*} {\left (x^{2} + 10 \, x + 25\right )} e^{\left (e^{\left (\frac {e^{\left (x^{2}\right )}}{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 29, normalized size = 1.38 \begin {gather*} {\left (x^{2} + 10 \, x + 25\right )} e^{\left (e^{\left (-x^{2} + \frac {x^{3} + e^{\left (x^{2}\right )}}{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \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 = 2.19, size = 19, normalized size = 0.90 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{\frac {{\mathrm {e}}^{x^2}}{x}}}\,\left (x^2+10\,x+25\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________