Optimal. Leaf size=25 \[ \frac {3 e^{-2 e^3} x \log (2)}{e^{1-4 x}-4 x} \]
________________________________________________________________________________________
Rubi [A] time = 0.29, antiderivative size = 27, normalized size of antiderivative = 1.08, number of steps used = 4, number of rules used = 3, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 6688, 6686} \begin {gather*} \frac {3 e^{1-2 e^3} \log (2)}{4 \left (e-4 e^{4 x} x\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log (2) \int \frac {e^{1-2 e^3-4 x} (3+12 x)}{e^{2-8 x}-8 e^{1-4 x} x+16 x^2} \, dx\\ &=\log (2) \int \frac {3 e^{1-2 e^3+4 x} (1+4 x)}{\left (e-4 e^{4 x} x\right )^2} \, dx\\ &=(3 \log (2)) \int \frac {e^{1-2 e^3+4 x} (1+4 x)}{\left (e-4 e^{4 x} x\right )^2} \, dx\\ &=\frac {3 e^{1-2 e^3} \log (2)}{4 \left (e-4 e^{4 x} x\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.04, size = 27, normalized size = 1.08 \begin {gather*} \frac {3 e^{1-2 e^3} \log (2)}{4 \left (e-4 e^{4 x} x\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 24, normalized size = 0.96 \begin {gather*} -\frac {3 \, x e^{\left (-2 \, e^{3}\right )} \log \relax (2)}{4 \, x - e^{\left (-4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 30, normalized size = 1.20 \begin {gather*} -\frac {3 \, e \log \relax (2)}{4 \, {\left (4 \, x e^{\left (4 \, x + 2 \, e^{3}\right )} - e^{\left (2 \, e^{3} + 1\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.14, size = 25, normalized size = 1.00
method | result | size |
risch | \(-\frac {3 \ln \relax (2) {\mathrm e}^{-2 \,{\mathrm e}^{3}} x}{4 x -{\mathrm e}^{-4 x +1}}\) | \(25\) |
norman | \(-\frac {3 \,{\mathrm e}^{-2 \,{\mathrm e}^{3}} \ln \relax (2) {\mathrm e}^{-4 x +1}}{4 \left (4 x -{\mathrm e}^{-4 x +1}\right )}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.45, size = 30, normalized size = 1.20 \begin {gather*} -\frac {3 \, e \log \relax (2)}{4 \, {\left (4 \, x e^{\left (4 \, x + 2 \, e^{3}\right )} - e^{\left (2 \, e^{3} + 1\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.54, size = 29, normalized size = 1.16 \begin {gather*} -\frac {3\,x\,\ln \relax (2)}{4\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^3}-{\mathrm {e}}^{2\,{\mathrm {e}}^3}\,{\mathrm {e}}^{-4\,x}\,\mathrm {e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 29, normalized size = 1.16 \begin {gather*} \frac {3 x \log {\relax (2 )}}{- 4 x e^{2 e^{3}} + e^{1 - 4 x} e^{2 e^{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________