Optimal. Leaf size=21 \[ e^x-2 e^{-11-e^5+\frac {x}{5}} x \]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 41, normalized size of antiderivative = 1.95, number of steps used = 5, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 2194, 2176} \begin {gather*} -2 e^{\frac {1}{5} \left (x-5 \left (11+e^5\right )\right )} (x+5)+e^x+10 e^{\frac {1}{5} \left (x-5 \left (11+e^5\right )\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (5 e^x+e^{\frac {1}{5} \left (-55-5 e^5+x\right )} (-10-2 x)\right ) \, dx\\ &=\frac {1}{5} \int e^{\frac {1}{5} \left (-55-5 e^5+x\right )} (-10-2 x) \, dx+\int e^x \, dx\\ &=e^x-2 e^{\frac {1}{5} \left (-5 \left (11+e^5\right )+x\right )} (5+x)+2 \int e^{\frac {1}{5} \left (-55-5 e^5+x\right )} \, dx\\ &=e^x+10 e^{\frac {1}{5} \left (-5 \left (11+e^5\right )+x\right )}-2 e^{\frac {1}{5} \left (-5 \left (11+e^5\right )+x\right )} (5+x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 21, normalized size = 1.00 \begin {gather*} e^x-2 e^{-11-e^5+\frac {x}{5}} x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.61, size = 16, normalized size = 0.76 \begin {gather*} -2 \, x e^{\left (\frac {1}{5} \, x - e^{5} - 11\right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 16, normalized size = 0.76 \begin {gather*} -2 \, x e^{\left (\frac {1}{5} \, x - e^{5} - 11\right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 17, normalized size = 0.81
method | result | size |
risch | \({\mathrm e}^{x}-2 \,{\mathrm e}^{-{\mathrm e}^{5}+\frac {x}{5}-11} x\) | \(17\) |
norman | \({\mathrm e}^{x}-2 \,{\mathrm e}^{-{\mathrm e}^{5}} {\mathrm e}^{-11} x \,{\mathrm e}^{\frac {x}{5}}\) | \(22\) |
meijerg | \(-1+{\mathrm e}^{x}+10 \,{\mathrm e}^{-{\mathrm e}^{5}-11} \left (1-{\mathrm e}^{\frac {x}{5}}\right )-10 \,{\mathrm e}^{-{\mathrm e}^{5}-11} \left (1-\frac {\left (-\frac {2 x}{5}+2\right ) {\mathrm e}^{\frac {x}{5}}}{2}\right )\) | \(44\) |
default | \(-10 \left (-{\mathrm e}^{5}+\frac {x}{5}-11\right ) {\mathrm e}^{-{\mathrm e}^{5}+\frac {x}{5}-11}-110 \,{\mathrm e}^{-{\mathrm e}^{5}+\frac {x}{5}-11}-10 \,{\mathrm e}^{-{\mathrm e}^{5}+\frac {x}{5}-11} {\mathrm e}^{5}+{\mathrm e}^{x}\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 30, normalized size = 1.43 \begin {gather*} -2 \, {\left (x - 5\right )} e^{\left (\frac {1}{5} \, x - e^{5} - 11\right )} + e^{x} - 10 \, e^{\left (\frac {1}{5} \, x - e^{5} - 11\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.09, size = 16, normalized size = 0.76 \begin {gather*} {\mathrm {e}}^x-2\,x\,{\mathrm {e}}^{\frac {x}{5}-{\mathrm {e}}^5-11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.17, size = 29, normalized size = 1.38 \begin {gather*} \frac {- 2 x \sqrt [5]{e^{x}} + e^{11} e^{x} e^{e^{5}}}{e^{11} e^{e^{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________