Optimal. Leaf size=29 \[ 1+e^{\frac {1}{4} \left (x+\left (4+4 \left (3-e^x\right )\right ) x\right ) (3-\log (2))} \]
________________________________________________________________________________________
Rubi [A] time = 0.56, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.055, Rules used = {12, 6741, 6706} \begin {gather*} 2^{-\frac {1}{4} \left (17-4 e^x\right ) x} e^{\frac {3}{4} \left (17-4 e^x\right ) x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6706
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \exp \left (\frac {1}{4} \left (51 x-17 x \log (2)+e^x (-12 x+4 x \log (2))\right )\right ) \left (51-17 \log (2)+e^x (-12-12 x+(4+4 x) \log (2))\right ) \, dx\\ &=\frac {1}{4} \int e^{\frac {1}{4} \left (-17+4 e^x\right ) x (-3+\log (2))} \left (17-4 e^x-4 e^x x\right ) (3-\log (2)) \, dx\\ &=\frac {1}{4} (3-\log (2)) \int e^{\frac {1}{4} \left (-17+4 e^x\right ) x (-3+\log (2))} \left (17-4 e^x-4 e^x x\right ) \, dx\\ &=2^{-\frac {1}{4} \left (17-4 e^x\right ) x} e^{\frac {3}{4} \left (17-4 e^x\right ) x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.50, size = 25, normalized size = 0.86 \begin {gather*} 2^{-17 x/4} e^{\frac {51 x}{4}+e^x x (-3+\log (2))} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.73, size = 21, normalized size = 0.72 \begin {gather*} e^{\left ({\left (x \log \relax (2) - 3 \, x\right )} e^{x} - \frac {17}{4} \, x \log \relax (2) + \frac {51}{4} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 21, normalized size = 0.72 \begin {gather*} e^{\left (x e^{x} \log \relax (2) - 3 \, x e^{x} - \frac {17}{4} \, x \log \relax (2) + \frac {51}{4} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.09, size = 23, normalized size = 0.79
method | result | size |
risch | \(2^{-\frac {17 x}{4}} 2^{{\mathrm e}^{x} x} {\mathrm e}^{-\frac {3 x \left (4 \,{\mathrm e}^{x}-17\right )}{4}}\) | \(23\) |
norman | \({\mathrm e}^{\frac {\left (4 x \ln \relax (2)-12 x \right ) {\mathrm e}^{x}}{4}-\frac {17 x \ln \relax (2)}{4}+\frac {51 x}{4}}\) | \(24\) |
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*} \frac {1}{4} \, \int {\left (4 \, {\left ({\left (x + 1\right )} \log \relax (2) - 3 \, x - 3\right )} e^{x} - 17 \, \log \relax (2) + 51\right )} e^{\left ({\left (x \log \relax (2) - 3 \, x\right )} e^{x} - \frac {17}{4} \, x \log \relax (2) + \frac {51}{4} \, x\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.18, size = 21, normalized size = 0.72 \begin {gather*} 2^{x\,{\mathrm {e}}^x-\frac {17\,x}{4}}\,{\mathrm {e}}^{-3\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{\frac {51\,x}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.28, size = 26, normalized size = 0.90 \begin {gather*} e^{- \frac {17 x \log {\relax (2 )}}{4} + \frac {51 x}{4} + \left (- 3 x + x \log {\relax (2 )}\right ) e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________