Integrand size = 20, antiderivative size = 12 \[ \int -\frac {1}{2} e^{5+\frac {1}{2} \left (2-e^5 x\right )} \, dx=e^{1-\frac {e^5 x}{2}} \]
[Out]
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 2234} \[ \int -\frac {1}{2} e^{5+\frac {1}{2} \left (2-e^5 x\right )} \, dx=e^{\frac {1}{2} \left (2-e^5 x\right )} \]
[In]
[Out]
Rule 12
Rule 2234
Rubi steps \begin{align*} \text {integral}& = -\left (\frac {1}{2} \int e^{5+\frac {1}{2} \left (2-e^5 x\right )} \, dx\right ) \\ & = e^{\frac {1}{2} \left (2-e^5 x\right )} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int -\frac {1}{2} e^{5+\frac {1}{2} \left (2-e^5 x\right )} \, dx=e^{1-\frac {e^5 x}{2}} \]
[In]
[Out]
Time = 0.10 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75
method | result | size |
gosper | \({\mathrm e}^{-\frac {x \,{\mathrm e}^{5}}{2}+1}\) | \(9\) |
derivativedivides | \({\mathrm e}^{-\frac {x \,{\mathrm e}^{5}}{2}+1}\) | \(9\) |
default | \({\mathrm e}^{-\frac {x \,{\mathrm e}^{5}}{2}+1}\) | \(9\) |
norman | \({\mathrm e}^{-\frac {x \,{\mathrm e}^{5}}{2}+1}\) | \(9\) |
risch | \({\mathrm e}^{-\frac {x \,{\mathrm e}^{5}}{2}+1}\) | \(9\) |
parallelrisch | \({\mathrm e}^{-\frac {x \,{\mathrm e}^{5}}{2}+1}\) | \(9\) |
parts | \({\mathrm e}^{-\frac {x \,{\mathrm e}^{5}}{2}+1}\) | \(9\) |
meijerg | \(-{\mathrm e} \left (1-{\mathrm e}^{-\frac {x \,{\mathrm e}^{5}}{2}}\right )\) | \(15\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {1}{2} e^{5+\frac {1}{2} \left (2-e^5 x\right )} \, dx=e^{\left (-\frac {1}{2} \, x e^{5} + 1\right )} \]
[In]
[Out]
Time = 0.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {1}{2} e^{5+\frac {1}{2} \left (2-e^5 x\right )} \, dx=e^{- \frac {x e^{5}}{2} + 1} \]
[In]
[Out]
none
Time = 0.17 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {1}{2} e^{5+\frac {1}{2} \left (2-e^5 x\right )} \, dx=e^{\left (-\frac {1}{2} \, x e^{5} + 1\right )} \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {1}{2} e^{5+\frac {1}{2} \left (2-e^5 x\right )} \, dx=e^{\left (-\frac {1}{2} \, x e^{5} + 1\right )} \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int -\frac {1}{2} e^{5+\frac {1}{2} \left (2-e^5 x\right )} \, dx=\mathrm {e}\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^5}{2}} \]
[In]
[Out]