Optimal. Leaf size=20 \[ \log \left (\frac {6}{5} e^{x-24 e^{-e^{625} x} x}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.09, antiderivative size = 13, normalized size of antiderivative = 0.65, number of steps used = 6, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {6742, 2194, 2176} \begin {gather*} x-24 e^{-e^{625} x} x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2176
Rule 2194
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\operatorname {Subst}\left (\int e^{-x} \left (-24+e^x+24 x\right ) \, dx,x,e^{625} x\right )}{e^{625}}\\ &=\frac {\operatorname {Subst}\left (\int \left (1-24 e^{-x}+24 e^{-x} x\right ) \, dx,x,e^{625} x\right )}{e^{625}}\\ &=x-\frac {24 \operatorname {Subst}\left (\int e^{-x} \, dx,x,e^{625} x\right )}{e^{625}}+\frac {24 \operatorname {Subst}\left (\int e^{-x} x \, dx,x,e^{625} x\right )}{e^{625}}\\ &=24 e^{-625-e^{625} x}+x-24 e^{-e^{625} x} x+\frac {24 \operatorname {Subst}\left (\int e^{-x} \, dx,x,e^{625} x\right )}{e^{625}}\\ &=x-24 e^{-e^{625} x} x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 13, normalized size = 0.65 \begin {gather*} x-24 e^{-e^{625} x} x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.77, size = 18, normalized size = 0.90 \begin {gather*} {\left (x e^{\left (x e^{625}\right )} - 24 \, x\right )} e^{\left (-x e^{625}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.21, size = 28, normalized size = 1.40 \begin {gather*} -24 \, {\left (x e^{625} + 1\right )} e^{\left (-x e^{625} - 625\right )} + x + 24 \, e^{\left (-x e^{625} - 625\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.10, size = 12, normalized size = 0.60
method | result | size |
risch | \(x -24 x \,{\mathrm e}^{-x \,{\mathrm e}^{625}}\) | \(12\) |
norman | \(\left (x \,{\mathrm e}^{x \,{\mathrm e}^{625}}-24 x \right ) {\mathrm e}^{-x \,{\mathrm e}^{625}}\) | \(20\) |
derivativedivides | \({\mathrm e}^{-625} \left (x \,{\mathrm e}^{625}-24 \,{\mathrm e}^{-x \,{\mathrm e}^{625}} x \,{\mathrm e}^{625}\right )\) | \(23\) |
default | \({\mathrm e}^{-625} \left (x \,{\mathrm e}^{625}-24 \,{\mathrm e}^{-x \,{\mathrm e}^{625}} x \,{\mathrm e}^{625}\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.38, size = 28, normalized size = 1.40 \begin {gather*} -24 \, {\left (x e^{625} + 1\right )} e^{\left (-x e^{625} - 625\right )} + x + 24 \, e^{\left (-x e^{625} - 625\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.07, size = 13, normalized size = 0.65 \begin {gather*} -x\,\left (24\,{\mathrm {e}}^{-x\,{\mathrm {e}}^{625}}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 10, normalized size = 0.50 \begin {gather*} x - 24 x e^{- x e^{625}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________