Integrand size = 109, antiderivative size = 28 \[ \int \frac {1}{2} e^{e^{\frac {2-x}{2}}-e^{2 x^3+2 e^x x^3+2 x^3 \log (x)}} \left (-e^{\frac {2-x}{2}}+e^{2 x^3+2 e^x x^3+2 x^3 \log (x)} \left (-16 x^2+e^x \left (-12 x^2-4 x^3\right )-12 x^2 \log (x)\right )\right ) \, dx=e^{e^{1-\frac {x}{2}}-e^{2 x^3 \left (1+e^x+\log (x)\right )}} \]
[Out]
Time = 1.01 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.39, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {12, 6838} \[ \int \frac {1}{2} e^{e^{\frac {2-x}{2}}-e^{2 x^3+2 e^x x^3+2 x^3 \log (x)}} \left (-e^{\frac {2-x}{2}}+e^{2 x^3+2 e^x x^3+2 x^3 \log (x)} \left (-16 x^2+e^x \left (-12 x^2-4 x^3\right )-12 x^2 \log (x)\right )\right ) \, dx=e^{e^{\frac {2-x}{2}}-e^{2 e^x x^3+2 x^3} x^{2 x^3}} \]
[In]
[Out]
Rule 12
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {1}{2} \int e^{e^{\frac {2-x}{2}}-e^{2 x^3+2 e^x x^3+2 x^3 \log (x)}} \left (-e^{\frac {2-x}{2}}+e^{2 x^3+2 e^x x^3+2 x^3 \log (x)} \left (-16 x^2+e^x \left (-12 x^2-4 x^3\right )-12 x^2 \log (x)\right )\right ) \, dx \\ & = e^{e^{\frac {2-x}{2}}-e^{2 x^3+2 e^x x^3} x^{2 x^3}} \\ \end{align*}
Time = 0.31 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.18 \[ \int \frac {1}{2} e^{e^{\frac {2-x}{2}}-e^{2 x^3+2 e^x x^3+2 x^3 \log (x)}} \left (-e^{\frac {2-x}{2}}+e^{2 x^3+2 e^x x^3+2 x^3 \log (x)} \left (-16 x^2+e^x \left (-12 x^2-4 x^3\right )-12 x^2 \log (x)\right )\right ) \, dx=e^{e^{1-\frac {x}{2}}-e^{2 \left (1+e^x\right ) x^3} x^{2 x^3}} \]
[In]
[Out]
Time = 3.22 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.82
method | result | size |
parallelrisch | \({\mathrm e}^{{\mathrm e}^{1-\frac {x}{2}}-{\mathrm e}^{2 x^{3} \left ({\mathrm e}^{x}+\ln \left (x \right )+1\right )}}\) | \(23\) |
risch | \({\mathrm e}^{-x^{2 x^{3}} {\mathrm e}^{2 x^{3} \left ({\mathrm e}^{x}+1\right )}+{\mathrm e}^{1-\frac {x}{2}}}\) | \(28\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (22) = 44\).
Time = 0.29 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.64 \[ \int \frac {1}{2} e^{e^{\frac {2-x}{2}}-e^{2 x^3+2 e^x x^3+2 x^3 \log (x)}} \left (-e^{\frac {2-x}{2}}+e^{2 x^3+2 e^x x^3+2 x^3 \log (x)} \left (-16 x^2+e^x \left (-12 x^2-4 x^3\right )-12 x^2 \log (x)\right )\right ) \, dx=e^{\left (-e^{\left (2 \, {\left (x^{3} e^{\left (-x + 2\right )} \log \left (x\right ) + x^{3} e^{2} + x^{3} e^{\left (-x + 2\right )}\right )} e^{\left (x - 2\right )}\right )} + e^{\left (-\frac {1}{2} \, x + 1\right )}\right )} \]
[In]
[Out]
Time = 5.50 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \frac {1}{2} e^{e^{\frac {2-x}{2}}-e^{2 x^3+2 e^x x^3+2 x^3 \log (x)}} \left (-e^{\frac {2-x}{2}}+e^{2 x^3+2 e^x x^3+2 x^3 \log (x)} \left (-16 x^2+e^x \left (-12 x^2-4 x^3\right )-12 x^2 \log (x)\right )\right ) \, dx=e^{- e^{2 x^{3} e^{x} + 2 x^{3} \log {\left (x \right )} + 2 x^{3}} + \frac {e}{\sqrt {e^{x}}}} \]
[In]
[Out]
\[ \int \frac {1}{2} e^{e^{\frac {2-x}{2}}-e^{2 x^3+2 e^x x^3+2 x^3 \log (x)}} \left (-e^{\frac {2-x}{2}}+e^{2 x^3+2 e^x x^3+2 x^3 \log (x)} \left (-16 x^2+e^x \left (-12 x^2-4 x^3\right )-12 x^2 \log (x)\right )\right ) \, dx=\int { -\frac {1}{2} \, {\left (4 \, {\left (3 \, x^{2} \log \left (x\right ) + 4 \, x^{2} + {\left (x^{3} + 3 \, x^{2}\right )} e^{x}\right )} e^{\left (2 \, x^{3} e^{x} + 2 \, x^{3} \log \left (x\right ) + 2 \, x^{3}\right )} + e^{\left (-\frac {1}{2} \, x + 1\right )}\right )} e^{\left (-e^{\left (2 \, x^{3} e^{x} + 2 \, x^{3} \log \left (x\right ) + 2 \, x^{3}\right )} + e^{\left (-\frac {1}{2} \, x + 1\right )}\right )} \,d x } \]
[In]
[Out]
\[ \int \frac {1}{2} e^{e^{\frac {2-x}{2}}-e^{2 x^3+2 e^x x^3+2 x^3 \log (x)}} \left (-e^{\frac {2-x}{2}}+e^{2 x^3+2 e^x x^3+2 x^3 \log (x)} \left (-16 x^2+e^x \left (-12 x^2-4 x^3\right )-12 x^2 \log (x)\right )\right ) \, dx=\int { -\frac {1}{2} \, {\left (4 \, {\left (3 \, x^{2} \log \left (x\right ) + 4 \, x^{2} + {\left (x^{3} + 3 \, x^{2}\right )} e^{x}\right )} e^{\left (2 \, x^{3} e^{x} + 2 \, x^{3} \log \left (x\right ) + 2 \, x^{3}\right )} + e^{\left (-\frac {1}{2} \, x + 1\right )}\right )} e^{\left (-e^{\left (2 \, x^{3} e^{x} + 2 \, x^{3} \log \left (x\right ) + 2 \, x^{3}\right )} + e^{\left (-\frac {1}{2} \, x + 1\right )}\right )} \,d x } \]
[In]
[Out]
Time = 8.37 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.18 \[ \int \frac {1}{2} e^{e^{\frac {2-x}{2}}-e^{2 x^3+2 e^x x^3+2 x^3 \log (x)}} \left (-e^{\frac {2-x}{2}}+e^{2 x^3+2 e^x x^3+2 x^3 \log (x)} \left (-16 x^2+e^x \left (-12 x^2-4 x^3\right )-12 x^2 \log (x)\right )\right ) \, dx={\mathrm {e}}^{{\mathrm {e}}^{-\frac {x}{2}}\,\mathrm {e}}\,{\mathrm {e}}^{-x^{2\,x^3}\,{\mathrm {e}}^{2\,x^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{2\,x^3}} \]
[In]
[Out]