Optimal. Leaf size=24 \[ -4-x+x \left (x-4 \left (x-9 e^{-x} (x+\log (x))\right )\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.26, antiderivative size = 42, normalized size of antiderivative = 1.75, number of steps used = 10, number of rules used = 4, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.121, Rules used = {6742, 2194, 2176, 2554} \begin {gather*} 36 e^{-x} x^2-3 x^2-x+36 e^{-x} \log (x)-36 e^{-x} (1-x) \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2176
Rule 2194
Rule 2554
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+36 e^{-x}-6 x+72 e^{-x} x-36 e^{-x} x^2-36 e^{-x} (-1+x) \log (x)\right ) \, dx\\ &=-x-3 x^2+36 \int e^{-x} \, dx-36 \int e^{-x} x^2 \, dx-36 \int e^{-x} (-1+x) \log (x) \, dx+72 \int e^{-x} x \, dx\\ &=-36 e^{-x}-x-72 e^{-x} x-3 x^2+36 e^{-x} x^2+36 e^{-x} \log (x)-36 e^{-x} (1-x) \log (x)-36 \int e^{-x} \, dx+72 \int e^{-x} \, dx-72 \int e^{-x} x \, dx\\ &=-72 e^{-x}-x-3 x^2+36 e^{-x} x^2+36 e^{-x} \log (x)-36 e^{-x} (1-x) \log (x)-72 \int e^{-x} \, dx\\ &=-x-3 x^2+36 e^{-x} x^2+36 e^{-x} \log (x)-36 e^{-x} (1-x) \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.14, size = 18, normalized size = 0.75 \begin {gather*} x \left (-1-3 x+36 e^{-x} (x+\log (x))\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.49, size = 27, normalized size = 1.12 \begin {gather*} {\left (36 \, x^{2} - {\left (3 \, x^{2} + x\right )} e^{x} + 36 \, x \log \relax (x)\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.12, size = 27, normalized size = 1.12 \begin {gather*} 36 \, x^{2} e^{\left (-x\right )} + 36 \, x e^{\left (-x\right )} \log \relax (x) - 3 \, x^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.11, size = 26, normalized size = 1.08
method | result | size |
default | \(-x +\left (36 x^{2}+36 x \ln \relax (x )\right ) {\mathrm e}^{-x}-3 x^{2}\) | \(26\) |
norman | \(\left (36 x^{2}+36 x \ln \relax (x )-{\mathrm e}^{x} x -3 \,{\mathrm e}^{x} x^{2}\right ) {\mathrm e}^{-x}\) | \(29\) |
risch | \(36 x \,{\mathrm e}^{-x} \ln \relax (x )-x \left (3 \,{\mathrm e}^{x} x -36 x +{\mathrm e}^{x}\right ) {\mathrm e}^{-x}\) | \(29\) |
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*} 36 \, {\left (x + 1\right )} e^{\left (-x\right )} \log \relax (x) - 3 \, x^{2} + 36 \, {\left (x^{2} + 2 \, x + 2\right )} e^{\left (-x\right )} - 72 \, {\left (x + 1\right )} e^{\left (-x\right )} - 36 \, e^{\left (-x\right )} \log \relax (x) - x + 36 \, {\rm Ei}\left (-x\right ) - 36 \, e^{\left (-x\right )} - 36 \, \int \frac {{\left (x + 1\right )} e^{\left (-x\right )}}{x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.27, size = 23, normalized size = 0.96 \begin {gather*} -x\,\left (3\,x-36\,x\,{\mathrm {e}}^{-x}-36\,{\mathrm {e}}^{-x}\,\ln \relax (x)+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.28, size = 20, normalized size = 0.83 \begin {gather*} - 3 x^{2} - x + \left (36 x^{2} + 36 x \log {\relax (x )}\right ) e^{- x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________