Integrand size = 28, antiderivative size = 20 \[ \int \left (-1+16 e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x}\right ) \, dx=e^5+e^{2 e^{4 e^{2 x}}}-x \]
[Out]
\[ \int \left (-1+16 e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x}\right ) \, dx=\int \left (-1+16 e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x}\right ) \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = -x+16 \int e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x} \, dx \\ & = -x+8 \text {Subst}\left (\int e^{2 \left (e^{4 x}+2 x\right )} \, dx,x,e^{2 x}\right ) \\ & = -x+4 \text {Subst}\left (\int e^{2 \left (e^{2 x}+x\right )} \, dx,x,2 e^{2 x}\right ) \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \left (-1+16 e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x}\right ) \, dx=e^{2 e^{4 e^{2 x}}}-x \]
[In]
[Out]
Time = 0.09 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75
method | result | size |
default | \(-x +{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2 x}}}\) | \(15\) |
norman | \(-x +{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2 x}}}\) | \(15\) |
risch | \(-x +{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2 x}}}\) | \(15\) |
parallelrisch | \(-x +{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2 x}}}\) | \(15\) |
parts | \(-x +{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2 x}}}\) | \(15\) |
derivativedivides | \(-\ln \left ({\mathrm e}^{x}\right )+{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2 x}}}\) | \(17\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (16) = 32\).
Time = 0.26 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.45 \[ \int \left (-1+16 e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x}\right ) \, dx=-{\left (x e^{\left (2 \, x + 4 \, e^{\left (2 \, x\right )}\right )} - e^{\left (2 \, x + 4 \, e^{\left (2 \, x\right )} + 2 \, e^{\left (4 \, e^{\left (2 \, x\right )}\right )}\right )}\right )} e^{\left (-2 \, x - 4 \, e^{\left (2 \, x\right )}\right )} \]
[In]
[Out]
Time = 0.10 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.60 \[ \int \left (-1+16 e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x}\right ) \, dx=- x + e^{2 e^{4 e^{2 x}}} \]
[In]
[Out]
none
Time = 0.19 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.70 \[ \int \left (-1+16 e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x}\right ) \, dx=-x + e^{\left (2 \, e^{\left (4 \, e^{\left (2 \, x\right )}\right )}\right )} \]
[In]
[Out]
\[ \int \left (-1+16 e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x}\right ) \, dx=\int { 16 \, e^{\left (2 \, x + 4 \, e^{\left (2 \, x\right )} + 2 \, e^{\left (4 \, e^{\left (2 \, x\right )}\right )}\right )} - 1 \,d x } \]
[In]
[Out]
Time = 0.12 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.70 \[ \int \left (-1+16 e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x}\right ) \, dx={\mathrm {e}}^{2\,{\mathrm {e}}^{4\,{\mathrm {e}}^{2\,x}}}-x \]
[In]
[Out]