Optimal. Leaf size=18 \[ \frac {5}{16} e^{-8-4 x} x^4 \log ^4(x) \]
________________________________________________________________________________________
Rubi [A] time = 0.23, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {12, 6741, 2288} \begin {gather*} \frac {5}{16} e^{-4 x-8} x^4 \log ^4(x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2288
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int e^{-8-4 x} x^3 \left (5 \log ^3(x)+(5-5 x) \log ^4(x)\right ) \, dx\\ &=\frac {1}{4} \int 5 e^{-8-4 x} x^3 \log ^3(x) (1+\log (x)-x \log (x)) \, dx\\ &=\frac {5}{4} \int e^{-8-4 x} x^3 \log ^3(x) (1+\log (x)-x \log (x)) \, dx\\ &=\frac {5}{16} e^{-8-4 x} x^4 \log ^4(x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.10, size = 18, normalized size = 1.00 \begin {gather*} \frac {5}{16} e^{-8-4 x} x^4 \log ^4(x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.66, size = 16, normalized size = 0.89 \begin {gather*} \frac {5}{16} \, e^{\left (-4 \, x + 4 \, \log \relax (x) - 8\right )} \log \relax (x)^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.14, size = 15, normalized size = 0.83 \begin {gather*} \frac {5}{16} \, x^{4} e^{\left (-4 \, x - 8\right )} \log \relax (x)^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 16, normalized size = 0.89
method | result | size |
risch | \(\frac {5 \ln \relax (x )^{4} x^{4} {\mathrm e}^{-4 x -8}}{16}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.52, size = 15, normalized size = 0.83 \begin {gather*} \frac {5}{16} \, x^{4} e^{\left (-4 \, x - 8\right )} \log \relax (x)^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {{\mathrm {e}}^{4\,\ln \relax (x)-4\,x-8}\,\left (5\,{\ln \relax (x)}^3-{\ln \relax (x)}^4\,\left (5\,x-5\right )\right )}{4\,x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.47, size = 19, normalized size = 1.06 \begin {gather*} \frac {5 x^{4} e^{- 4 x - 8} \log {\relax (x )}^{4}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________