Integrand size = 77, antiderivative size = 28 \[ \int \frac {e^{e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}}+x} \left (-x^4+e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}} \left (-768+3 x^6-x^4 \log (5)\right )\right )}{x^4} \, dx=1-e^{e^{x \left (-\left (\frac {16}{x^2}-x\right )^2+\log (5)\right )}+x} \]
[Out]
Time = 0.49 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {6838} \[ \int \frac {e^{e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}}+x} \left (-x^4+e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}} \left (-768+3 x^6-x^4 \log (5)\right )\right )}{x^4} \, dx=-e^{5^x e^{-\frac {x^6-32 x^3+256}{x^3}}+x} \]
[In]
[Out]
Rule 6838
Rubi steps \begin{align*} \text {integral}& = -e^{5^x e^{-\frac {256-32 x^3+x^6}{x^3}}+x} \\ \end{align*}
Time = 5.13 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int \frac {e^{e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}}+x} \left (-x^4+e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}} \left (-768+3 x^6-x^4 \log (5)\right )\right )}{x^4} \, dx=-e^{5^x e^{32-\frac {256}{x^3}-x^3}+x} \]
[In]
[Out]
Time = 5.17 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.82
method | result | size |
risch | \(-{\mathrm e}^{5^{x} {\mathrm e}^{-\frac {\left (x^{3}-16\right )^{2}}{x^{3}}}+x}\) | \(23\) |
norman | \(-{\mathrm e}^{{\mathrm e}^{\frac {x^{4} \ln \left (5\right )-x^{6}+32 x^{3}-256}{x^{3}}}+x}\) | \(29\) |
parallelrisch | \(-{\mathrm e}^{{\mathrm e}^{\frac {x^{4} \ln \left (5\right )-x^{6}+32 x^{3}-256}{x^{3}}}+x}\) | \(29\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {e^{e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}}+x} \left (-x^4+e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}} \left (-768+3 x^6-x^4 \log (5)\right )\right )}{x^4} \, dx=-e^{\left (x + e^{\left (-\frac {x^{6} - x^{4} \log \left (5\right ) - 32 \, x^{3} + 256}{x^{3}}\right )}\right )} \]
[In]
[Out]
Time = 0.22 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {e^{e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}}+x} \left (-x^4+e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}} \left (-768+3 x^6-x^4 \log (5)\right )\right )}{x^4} \, dx=- e^{x + e^{\frac {- x^{6} + x^{4} \log {\left (5 \right )} + 32 x^{3} - 256}{x^{3}}}} \]
[In]
[Out]
\[ \int \frac {e^{e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}}+x} \left (-x^4+e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}} \left (-768+3 x^6-x^4 \log (5)\right )\right )}{x^4} \, dx=\int { -\frac {{\left (x^{4} - {\left (3 \, x^{6} - x^{4} \log \left (5\right ) - 768\right )} e^{\left (-\frac {x^{6} - x^{4} \log \left (5\right ) - 32 \, x^{3} + 256}{x^{3}}\right )}\right )} e^{\left (x + e^{\left (-\frac {x^{6} - x^{4} \log \left (5\right ) - 32 \, x^{3} + 256}{x^{3}}\right )}\right )}}{x^{4}} \,d x } \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.79 \[ \int \frac {e^{e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}}+x} \left (-x^4+e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}} \left (-768+3 x^6-x^4 \log (5)\right )\right )}{x^4} \, dx=-e^{\left (x + e^{\left (-x^{3} + x \log \left (5\right ) - \frac {256}{x^{3}} + 32\right )}\right )} \]
[In]
[Out]
Time = 9.02 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.82 \[ \int \frac {e^{e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}}+x} \left (-x^4+e^{\frac {-256+32 x^3-x^6+x^4 \log (5)}{x^3}} \left (-768+3 x^6-x^4 \log (5)\right )\right )}{x^4} \, dx=-{\mathrm {e}}^{5^x\,{\mathrm {e}}^{32}\,{\mathrm {e}}^{-x^3}\,{\mathrm {e}}^{-\frac {256}{x^3}}}\,{\mathrm {e}}^x \]
[In]
[Out]