Optimal. Leaf size=26 \[ 4 \left (3-\frac {1}{3} x \log (5)+e^{-x} \log (x)-\frac {1}{3} x \log (x)\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.36, antiderivative size = 31, normalized size of antiderivative = 1.19, number of steps
used = 7, number of rules used = 5, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 6873, 6874,
2332, 2326} \begin {gather*} \frac {4 x}{3}-\frac {4}{3} x \log (x)-\frac {4}{3} x (1+\log (5))+4 e^{-x} \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2326
Rule 2332
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {e^{-x} \left (12+e^x (-4 x-4 x \log (5))+\left (-12 x-4 e^x x\right ) \log (x)\right )}{x} \, dx\\ &=\frac {1}{3} \int \frac {4 e^{-x} \left (3-e^x x (1+\log (5))-3 x \log (x)-e^x x \log (x)\right )}{x} \, dx\\ &=\frac {4}{3} \int \frac {e^{-x} \left (3-e^x x (1+\log (5))-3 x \log (x)-e^x x \log (x)\right )}{x} \, dx\\ &=\frac {4}{3} \int \left (-1-\log (5)-\log (x)-\frac {3 e^{-x} (-1+x \log (x))}{x}\right ) \, dx\\ &=-\frac {4}{3} x (1+\log (5))-\frac {4}{3} \int \log (x) \, dx-4 \int \frac {e^{-x} (-1+x \log (x))}{x} \, dx\\ &=\frac {4 x}{3}-\frac {4}{3} x (1+\log (5))+4 e^{-x} \log (x)-\frac {4}{3} x \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.07, size = 22, normalized size = 0.85 \begin {gather*} -\frac {4}{3} \left (x \log (5)-3 e^{-x} \log (x)+x \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.61, size = 20, normalized size = 0.77
method | result | size |
default | \(4 \ln \left (x \right ) {\mathrm e}^{-x}-\frac {4 x \ln \left (5\right )}{3}-\frac {4 x \ln \left (x \right )}{3}\) | \(20\) |
risch | \(-\frac {4 \left ({\mathrm e}^{x} x -3\right ) {\mathrm e}^{-x} \ln \left (x \right )}{3}-\frac {4 x \ln \left (5\right )}{3}\) | \(21\) |
norman | \(\left (-\frac {4 x \,{\mathrm e}^{x} \ln \left (5\right )}{3}-\frac {4 x \,{\mathrm e}^{x} \ln \left (x \right )}{3}+4 \ln \left (x \right )\right ) {\mathrm e}^{-x}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 19, normalized size = 0.73 \begin {gather*} -\frac {4}{3} \, x \log \left (5\right ) - \frac {4}{3} \, x \log \left (x\right ) + 4 \, e^{\left (-x\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.34, size = 22, normalized size = 0.85 \begin {gather*} -\frac {4}{3} \, {\left (x e^{x} \log \left (5\right ) + {\left (x e^{x} - 3\right )} \log \left (x\right )\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.12, size = 24, normalized size = 0.92 \begin {gather*} - \frac {4 x \log {\left (x \right )}}{3} - \frac {4 x \log {\left (5 \right )}}{3} + 4 e^{- x} \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 19, normalized size = 0.73 \begin {gather*} -\frac {4}{3} \, x \log \left (5\right ) - \frac {4}{3} \, x \log \left (x\right ) + 4 \, e^{\left (-x\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.25, size = 19, normalized size = 0.73 \begin {gather*} 4\,{\mathrm {e}}^{-x}\,\ln \left (x\right )-\frac {4\,x\,\ln \left (5\right )}{3}-\frac {4\,x\,\ln \left (x\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________