Optimal. Leaf size=19 \[ 2-\log (259)+e^{-x} (-5+x) \log \left (x^2\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.24, antiderivative size = 27, normalized size of antiderivative = 1.42, number of steps
used = 12, number of rules used = 7, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {6874, 2230,
2225, 2209, 2207, 2634, 12} \begin {gather*} e^{-x} \log \left (x^2\right )-e^{-x} (6-x) \log \left (x^2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2207
Rule 2209
Rule 2225
Rule 2230
Rule 2634
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 e^{-x} (-5+x)}{x}-e^{-x} (-6+x) \log \left (x^2\right )\right ) \, dx\\ &=2 \int \frac {e^{-x} (-5+x)}{x} \, dx-\int e^{-x} (-6+x) \log \left (x^2\right ) \, dx\\ &=e^{-x} \log \left (x^2\right )-e^{-x} (6-x) \log \left (x^2\right )+2 \int \left (e^{-x}-\frac {5 e^{-x}}{x}\right ) \, dx+\int \frac {2 e^{-x} (5-x)}{x} \, dx\\ &=e^{-x} \log \left (x^2\right )-e^{-x} (6-x) \log \left (x^2\right )+2 \int e^{-x} \, dx+2 \int \frac {e^{-x} (5-x)}{x} \, dx-10 \int \frac {e^{-x}}{x} \, dx\\ &=-2 e^{-x}-10 \text {Ei}(-x)+e^{-x} \log \left (x^2\right )-e^{-x} (6-x) \log \left (x^2\right )+2 \int \left (-e^{-x}+\frac {5 e^{-x}}{x}\right ) \, dx\\ &=-2 e^{-x}-10 \text {Ei}(-x)+e^{-x} \log \left (x^2\right )-e^{-x} (6-x) \log \left (x^2\right )-2 \int e^{-x} \, dx+10 \int \frac {e^{-x}}{x} \, dx\\ &=e^{-x} \log \left (x^2\right )-e^{-x} (6-x) \log \left (x^2\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 13, normalized size = 0.68 \begin {gather*} e^{-x} (-5+x) \log \left (x^2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.05, size = 29, normalized size = 1.53
method | result | size |
norman | \(\left (x \ln \left (x^{2}\right )-5 \ln \left (x^{2}\right )\right ) {\mathrm e}^{-x}\) | \(19\) |
default | \(\left (x \left (\ln \left (x^{2}\right )-2 \ln \left (x \right )\right )-5 \ln \left (x^{2}\right )+2 x \ln \left (x \right )\right ) {\mathrm e}^{-x}\) | \(29\) |
risch | \(2 \left (x -5\right ) {\mathrm e}^{-x} \ln \left (x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (x \mathrm {csgn}\left (i x \right )^{2}-2 x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )+x \mathrm {csgn}\left (i x^{2}\right )^{2}-5 \mathrm {csgn}\left (i x \right )^{2}+10 \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )-5 \mathrm {csgn}\left (i x^{2}\right )^{2}\right ) {\mathrm e}^{-x}}{2}\) | \(98\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 12, normalized size = 0.63 \begin {gather*} {\left (x - 5\right )} e^{\left (-x\right )} \log \left (x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.10, size = 15, normalized size = 0.79 \begin {gather*} \left (x \log {\left (x^{2} \right )} - 5 \log {\left (x^{2} \right )}\right ) e^{- x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 21, normalized size = 1.11 \begin {gather*} x e^{\left (-x\right )} \log \left (x^{2}\right ) - 5 \, e^{\left (-x\right )} \log \left (x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 7.29, size = 12, normalized size = 0.63 \begin {gather*} \ln \left (x^2\right )\,{\mathrm {e}}^{-x}\,\left (x-5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________