Optimal. Leaf size=22 \[ e^{\frac {1}{1+6 x+\frac {1}{3} (1-x-\log (4))}} \]
________________________________________________________________________________________
Rubi [A] time = 0.10, antiderivative size = 15, normalized size of antiderivative = 0.68, number of steps used = 3, number of rules used = 3, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 6688, 2209} \begin {gather*} e^{\frac {3}{17 x+4-\log (4)}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2209
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (51 \int \frac {e^{-\frac {3}{-4-17 x+\log (4)}}}{16+136 x+289 x^2+(-8-34 x) \log (4)+\log ^2(4)} \, dx\right )\\ &=-\left (51 \int \frac {e^{\frac {3}{4+17 x-\log (4)}}}{(4+17 x-\log (4))^2} \, dx\right )\\ &=e^{\frac {3}{4+17 x-\log (4)}}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 15, normalized size = 0.68 \begin {gather*} e^{\frac {3}{4+17 x-\log (4)}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.50, size = 14, normalized size = 0.64 \begin {gather*} e^{\left (\frac {3}{17 \, x - 2 \, \log \relax (2) + 4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.22, size = 14, normalized size = 0.64 \begin {gather*} e^{\left (\frac {3}{17 \, x - 2 \, \log \relax (2) + 4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.11, size = 15, normalized size = 0.68
method | result | size |
gosper | \({\mathrm e}^{-\frac {3}{2 \ln \relax (2)-17 x -4}}\) | \(15\) |
derivativedivides | \({\mathrm e}^{\frac {3}{-2 \ln \relax (2)+17 x +4}}\) | \(15\) |
default | \({\mathrm e}^{\frac {3}{-2 \ln \relax (2)+17 x +4}}\) | \(15\) |
risch | \({\mathrm e}^{-\frac {3}{2 \ln \relax (2)-17 x -4}}\) | \(15\) |
norman | \(\frac {\left (2 \ln \relax (2)-4\right ) {\mathrm e}^{-\frac {3}{2 \ln \relax (2)-17 x -4}}-17 x \,{\mathrm e}^{-\frac {3}{2 \ln \relax (2)-17 x -4}}}{2 \ln \relax (2)-17 x -4}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.46, size = 14, normalized size = 0.64 \begin {gather*} e^{\left (\frac {3}{17 \, x - 2 \, \log \relax (2) + 4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.39, size = 14, normalized size = 0.64 \begin {gather*} {\mathrm {e}}^{\frac {3}{17\,x-\ln \relax (4)+4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.27, size = 14, normalized size = 0.64 \begin {gather*} e^{- \frac {3}{- 17 x - 4 + 2 \log {\relax (2 )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________