Optimal. Leaf size=26 \[ \left (e^{3 x}-2 e^{e^{-e^{4 x}} x}+2 x\right )^2 \]
________________________________________________________________________________________
Rubi [A] time = 1.23, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 150, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6688, 12, 6686} \begin {gather*} \left (2 x+e^{3 x}-2 e^{e^{-e^{4 x}} x}\right )^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int 2 e^{-e^{4 x}} \left (e^{3 x}-2 e^{e^{-e^{4 x}} x}+2 x\right ) \left (2 e^{e^{4 x}}-2 e^{e^{-e^{4 x}} x}+3 e^{e^{4 x}+3 x}+8 e^{\left (4+e^{-e^{4 x}}\right ) x} x\right ) \, dx\\ &=2 \int e^{-e^{4 x}} \left (e^{3 x}-2 e^{e^{-e^{4 x}} x}+2 x\right ) \left (2 e^{e^{4 x}}-2 e^{e^{-e^{4 x}} x}+3 e^{e^{4 x}+3 x}+8 e^{\left (4+e^{-e^{4 x}}\right ) x} x\right ) \, dx\\ &=\left (e^{3 x}-2 e^{e^{-e^{4 x}} x}+2 x\right )^2\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.07, size = 26, normalized size = 1.00 \begin {gather*} \left (e^{3 x}-2 e^{e^{-e^{4 x}} x}+2 x\right )^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.49, size = 66, normalized size = 2.54 \begin {gather*} 4 \, x^{2} - 2 \, {\left (2 \, x + e^{\left (3 \, x\right )}\right )} e^{\left ({\left (e^{\left (e^{\left (4 \, x\right )}\right )} \log \relax (2) + x\right )} e^{\left (-e^{\left (4 \, x\right )}\right )}\right )} + 4 \, x e^{\left (3 \, x\right )} + e^{\left (2 \, {\left (e^{\left (e^{\left (4 \, x\right )}\right )} \log \relax (2) + x\right )} e^{\left (-e^{\left (4 \, x\right )}\right )}\right )} + e^{\left (6 \, x\right )} \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 -2 \, {\left ({\left (4 \, x e^{\left (4 \, x\right )} - 1\right )} e^{\left (2 \, {\left (e^{\left (e^{\left (4 \, x\right )}\right )} \log \relax (2) + x\right )} e^{\left (-e^{\left (4 \, x\right )}\right )}\right )} - {\left (4 \, {\left (2 \, x^{2} + x e^{\left (3 \, x\right )}\right )} e^{\left (4 \, x\right )} - {\left (3 \, e^{\left (3 \, x\right )} + 2\right )} e^{\left (e^{\left (4 \, x\right )}\right )} - 2 \, x - e^{\left (3 \, x\right )}\right )} e^{\left ({\left (e^{\left (e^{\left (4 \, x\right )}\right )} \log \relax (2) + x\right )} e^{\left (-e^{\left (4 \, x\right )}\right )}\right )} - {\left (2 \, {\left (3 \, x + 1\right )} e^{\left (3 \, x\right )} + 4 \, x + 3 \, e^{\left (6 \, x\right )}\right )} e^{\left (e^{\left (4 \, x\right )}\right )}\right )} e^{\left (-e^{\left (4 \, x\right )}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.08, size = 53, normalized size = 2.04
method | result | size |
risch | \({\mathrm e}^{6 x}+4 x \,{\mathrm e}^{3 x}+4 x^{2}+4 \,{\mathrm e}^{2 \,{\mathrm e}^{-{\mathrm e}^{4 x}} x}+2 \left (-2 \,{\mathrm e}^{3 x}-4 x \right ) {\mathrm e}^{{\mathrm e}^{-{\mathrm e}^{4 x}} x}\) | \(53\) |
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*} 4 \, x^{2} + \frac {4}{3} \, {\left (3 \, x - 1\right )} e^{\left (3 \, x\right )} + 4 \, e^{\left (2 \, x e^{\left (-e^{\left (4 \, x\right )}\right )}\right )} + e^{\left (6 \, x\right )} + \frac {4}{3} \, e^{\left (3 \, x\right )} - 2 \, \int -2 \, {\left (8 \, x^{2} e^{\left (4 \, x\right )} + 4 \, x e^{\left (7 \, x\right )} - {\left (3 \, e^{\left (3 \, x\right )} + 2\right )} e^{\left (e^{\left (4 \, x\right )}\right )} - 2 \, x - e^{\left (3 \, x\right )}\right )} e^{\left (x e^{\left (-e^{\left (4 \, x\right )}\right )} - e^{\left (4 \, x\right )}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} -\int {\mathrm {e}}^{-{\mathrm {e}}^{4\,x}}\,\left ({\mathrm {e}}^{{\mathrm {e}}^{-{\mathrm {e}}^{4\,x}}\,\left (x+{\mathrm {e}}^{{\mathrm {e}}^{4\,x}}\,\ln \relax (2)\right )}\,\left (4\,x+2\,{\mathrm {e}}^{3\,x}-{\mathrm {e}}^{4\,x}\,\left (8\,x\,{\mathrm {e}}^{3\,x}+16\,x^2\right )+{\mathrm {e}}^{{\mathrm {e}}^{4\,x}}\,\left (6\,{\mathrm {e}}^{3\,x}+4\right )\right )-{\mathrm {e}}^{{\mathrm {e}}^{4\,x}}\,\left (8\,x+6\,{\mathrm {e}}^{6\,x}+{\mathrm {e}}^{3\,x}\,\left (12\,x+4\right )\right )+{\mathrm {e}}^{2\,{\mathrm {e}}^{-{\mathrm {e}}^{4\,x}}\,\left (x+{\mathrm {e}}^{{\mathrm {e}}^{4\,x}}\,\ln \relax (2)\right )}\,\left (8\,x\,{\mathrm {e}}^{4\,x}-2\right )\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________