Optimal. Leaf size=21 \[ \frac {e^{e^{2 (78-x+4 (3+\log (x)))}}}{x} \]
________________________________________________________________________________________
Rubi [B] time = 0.08, antiderivative size = 54, normalized size of antiderivative = 2.57, number of steps used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {2288} \begin {gather*} \frac {e^{e^{180-2 x} x^8-2 x+180} (4-x) x^6}{4 e^{180-2 x} x^7-e^{180-2 x} x^8} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{180-2 x+e^{180-2 x} x^8} (4-x) x^6}{4 e^{180-2 x} x^7-e^{180-2 x} x^8}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.26, size = 17, normalized size = 0.81 \begin {gather*} \frac {e^{e^{180-2 x} x^8}}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 15, normalized size = 0.71 \begin {gather*} \frac {e^{\left (e^{\left (-2 \, x + 8 \, \log \relax (x) + 180\right )}\right )}}{x} \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*} \int -\frac {{\left (2 \, {\left (x - 4\right )} e^{\left (-2 \, x + 8 \, \log \relax (x) + 180\right )} + 1\right )} e^{\left (e^{\left (-2 \, x + 8 \, \log \relax (x) + 180\right )}\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.09, size = 16, normalized size = 0.76
method | result | size |
norman | \(\frac {{\mathrm e}^{{\mathrm e}^{8 \ln \relax (x )-2 x +180}}}{x}\) | \(16\) |
risch | \(\frac {{\mathrm e}^{x^{8} {\mathrm e}^{180-2 x}}}{x}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\int \frac {{\left (2 \, {\left (x - 4\right )} x^{8} e^{\left (-2 \, x + 180\right )} + 1\right )} e^{\left (x^{8} e^{\left (-2 \, x + 180\right )}\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.17, size = 15, normalized size = 0.71 \begin {gather*} \frac {{\mathrm {e}}^{x^8\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{180}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 12, normalized size = 0.57 \begin {gather*} \frac {e^{x^{8} e^{180 - 2 x}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________