Optimal. Leaf size=30 \[ -3-e^{-2+3 \left (6-e^x\right )+\frac {e^{x/8}}{\log (5)}}+x \]
________________________________________________________________________________________
Rubi [A] time = 0.18, antiderivative size = 25, normalized size of antiderivative = 0.83, number of steps used = 6, number of rules used = 4, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.070, Rules used = {12, 2274, 2282, 6706} \begin {gather*} x-e^{-3 e^x+\frac {e^{x/8}}{\log (5)}+16} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2274
Rule 2282
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (8 \log (5)+e^{\frac {e^{x/8}+16 \log (5)-3 e^x \log (5)}{\log (5)}} \left (-e^{x/8}+24 e^x \log (5)\right )\right ) \, dx}{8 \log (5)}\\ &=x+\frac {\int e^{\frac {e^{x/8}+16 \log (5)-3 e^x \log (5)}{\log (5)}} \left (-e^{x/8}+24 e^x \log (5)\right ) \, dx}{8 \log (5)}\\ &=x+\frac {\int 5^{\frac {16}{\log (5)}} e^{\frac {e^{x/8}-3 e^x \log (5)}{\log (5)}} \left (-e^{x/8}+24 e^x \log (5)\right ) \, dx}{8 \log (5)}\\ &=x+\frac {e^{16} \int e^{\frac {e^{x/8}-3 e^x \log (5)}{\log (5)}} \left (-e^{x/8}+24 e^x \log (5)\right ) \, dx}{8 \log (5)}\\ &=x+\frac {e^{16} \operatorname {Subst}\left (\int e^{-3 x^8+\frac {x}{\log (5)}} \left (-1+24 x^7 \log (5)\right ) \, dx,x,e^{x/8}\right )}{\log (5)}\\ &=-e^{16-3 e^x+\frac {e^{x/8}}{\log (5)}}+x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.15, size = 25, normalized size = 0.83 \begin {gather*} -e^{16-3 e^x+\frac {e^{x/8}}{\log (5)}}+x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.78, size = 28, normalized size = 0.93 \begin {gather*} x - e^{\left (-\frac {3 \, e^{x} \log \relax (5) - e^{\left (\frac {1}{8} \, x\right )} - 16 \, \log \relax (5)}{\log \relax (5)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.22, size = 30, normalized size = 1.00 \begin {gather*} \frac {x \log \relax (5) - e^{\left (\frac {e^{\left (\frac {1}{8} \, x\right )}}{\log \relax (5)} - 3 \, e^{x} + 16\right )} \log \relax (5)}{\log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.20, size = 29, normalized size = 0.97
method | result | size |
risch | \(x -{\mathrm e}^{-\frac {3 \,{\mathrm e}^{x} \ln \relax (5)-16 \ln \relax (5)-{\mathrm e}^{\frac {x}{8}}}{\ln \relax (5)}}\) | \(29\) |
norman | \(x -{\mathrm e}^{\frac {-3 \,{\mathrm e}^{x} \ln \relax (5)+{\mathrm e}^{\frac {x}{8}}+16 \ln \relax (5)}{\ln \relax (5)}}\) | \(30\) |
default | \(\frac {-8 \ln \relax (5) {\mathrm e}^{\frac {-3 \,{\mathrm e}^{x} \ln \relax (5)+{\mathrm e}^{\frac {x}{8}}+16 \ln \relax (5)}{\ln \relax (5)}}+8 x \ln \relax (5)}{8 \ln \relax (5)}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.82, size = 30, normalized size = 1.00 \begin {gather*} \frac {x \log \relax (5) - e^{\left (\frac {e^{\left (\frac {1}{8} \, x\right )}}{\log \relax (5)} - 3 \, e^{x} + 16\right )} \log \relax (5)}{\log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.28, size = 21, normalized size = 0.70 \begin {gather*} x-{\mathrm {e}}^{16}\,{\mathrm {e}}^{-3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{\frac {{\left ({\mathrm {e}}^x\right )}^{1/8}}{\ln \relax (5)}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.23, size = 24, normalized size = 0.80 \begin {gather*} x - e^{\frac {e^{\frac {x}{8}} - 3 e^{x} \log {\relax (5 )} + 16 \log {\relax (5 )}}{\log {\relax (5 )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________