Optimal. Leaf size=24 \[ \log \left (e^{1-x+x^2 \left (-\frac {1}{3} x \log (5)+\log (-4+x)\right )}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.15, antiderivative size = 21, normalized size of antiderivative = 0.88, number of steps used = 7, number of rules used = 4, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {6742, 1850, 2395, 43} \begin {gather*} -\frac {1}{3} x^3 \log (5)+x^2 \log (x-4)-x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rule 1850
Rule 2395
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-4+x+x^3 \log (5)-x^2 (1+\log (625))}{4-x}+2 x \log (-4+x)\right ) \, dx\\ &=2 \int x \log (-4+x) \, dx+\int \frac {-4+x+x^3 \log (5)-x^2 (1+\log (625))}{4-x} \, dx\\ &=x^2 \log (-4+x)-\int \frac {x^2}{-4+x} \, dx+\int \left (3+\frac {16}{-4+x}+x-x^2 \log (5)\right ) \, dx\\ &=3 x+\frac {x^2}{2}-\frac {1}{3} x^3 \log (5)+16 \log (4-x)+x^2 \log (-4+x)-\int \left (4+\frac {16}{-4+x}+x\right ) \, dx\\ &=-x-\frac {1}{3} x^3 \log (5)+x^2 \log (-4+x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 21, normalized size = 0.88 \begin {gather*} -x-\frac {1}{3} x^3 \log (5)+x^2 \log (-4+x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.69, size = 19, normalized size = 0.79 \begin {gather*} -\frac {1}{3} \, x^{3} \log \relax (5) + x^{2} \log \left (x - 4\right ) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 19, normalized size = 0.79 \begin {gather*} -\frac {1}{3} \, x^{3} \log \relax (5) + x^{2} \log \left (x - 4\right ) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.10, size = 20, normalized size = 0.83
method | result | size |
norman | \(x^{2} \ln \left (x -4\right )-x -\frac {x^{3} \ln \relax (5)}{3}\) | \(20\) |
risch | \(x^{2} \ln \left (x -4\right )-x -\frac {x^{3} \ln \relax (5)}{3}\) | \(20\) |
derivativedivides | \(-\frac {\ln \relax (5) \left (x -4\right )^{3}}{3}-4 \ln \relax (5) \left (x -4\right )^{2}+\ln \left (x -4\right ) \left (x -4\right )^{2}-16 \left (x -4\right ) \ln \relax (5)+8 \left (x -4\right ) \ln \left (x -4\right )-x +4+16 \ln \left (x -4\right )\) | \(56\) |
default | \(-\frac {\ln \relax (5) \left (x -4\right )^{3}}{3}-4 \ln \relax (5) \left (x -4\right )^{2}+\ln \left (x -4\right ) \left (x -4\right )^{2}-16 \left (x -4\right ) \ln \relax (5)+8 \left (x -4\right ) \ln \left (x -4\right )-x +4+16 \ln \left (x -4\right )\) | \(56\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.38, size = 75, normalized size = 3.12 \begin {gather*} -\frac {1}{3} \, {\left (x^{3} + 6 \, x^{2} + 48 \, x + 192 \, \log \left (x - 4\right )\right )} \log \relax (5) + 2 \, {\left (x^{2} + 8 \, x + 32 \, \log \left (x - 4\right )\right )} \log \relax (5) + {\left (x^{2} + 8 \, x + 32 \, \log \left (x - 4\right )\right )} \log \left (x - 4\right ) - 8 \, {\left (x + 4 \, \log \left (x - 4\right )\right )} \log \left (x - 4\right ) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.14, size = 19, normalized size = 0.79 \begin {gather*} x^2\,\ln \left (x-4\right )-x-\frac {x^3\,\ln \relax (5)}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.14, size = 17, normalized size = 0.71 \begin {gather*} - \frac {x^{3} \log {\relax (5 )}}{3} + x^{2} \log {\left (x - 4 \right )} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________