Optimal. Leaf size=21 \[ e^4+\frac {e^{-3-x} x}{\log (5) \log ^2(x)} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 17, normalized size of antiderivative = 0.81, number of steps
used = 2, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 2232}
\begin {gather*} \frac {e^{-x-3} x}{\log (5) \log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2232
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{-3-x} (-2+(1-x) \log (x))}{\log ^3(x)} \, dx}{\log (5)}\\ &=\frac {e^{-3-x} x}{\log (5) \log ^2(x)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 17, normalized size = 0.81 \begin {gather*} \frac {e^{-3-x} x}{\log (5) \log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.24, size = 17, normalized size = 0.81
method | result | size |
norman | \(\frac {x \,{\mathrm e}^{-3-x}}{\ln \left (x \right )^{2} \ln \left (5\right )}\) | \(17\) |
risch | \(\frac {x \,{\mathrm e}^{-3-x}}{\ln \left (x \right )^{2} \ln \left (5\right )}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.42, size = 16, normalized size = 0.76 \begin {gather*} \frac {x e^{\left (-x - 3\right )}}{\log \left (5\right ) \log \left (x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 16, normalized size = 0.76 \begin {gather*} \frac {x e^{\left (-x - 3\right )}}{\log \left (5\right ) \log \left (x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 15, normalized size = 0.71 \begin {gather*} \frac {x e^{- x - 3}}{\log {\left (5 \right )} \log {\left (x \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 16, normalized size = 0.76 \begin {gather*} \frac {x e^{\left (-x - 3\right )}}{\log \left (5\right ) \log \left (x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.39, size = 16, normalized size = 0.76 \begin {gather*} \frac {x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-3}}{\ln \left (5\right )\,{\ln \left (x\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________