Optimal. Leaf size=13 \[ 4 e^3 (-3+\log (5-20 x)) \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.85, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 31} \begin {gather*} 4 e^3 \log (1-4 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 31
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (16 e^3\right ) \int \frac {1}{-1+4 x} \, dx\\ &=4 e^3 \log (1-4 x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 11, normalized size = 0.85 \begin {gather*} 4 e^3 \log (-1+4 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.91, size = 10, normalized size = 0.77 \begin {gather*} 4 \, e^{3} \log \left (4 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 11, normalized size = 0.85 \begin {gather*} 4 \, e^{3} \log \left ({\left | 4 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.15, size = 11, normalized size = 0.85
method | result | size |
default | \(4 \,{\mathrm e}^{3} \ln \left (4 x -1\right )\) | \(11\) |
norman | \(4 \,{\mathrm e}^{3} \ln \left (4 x -1\right )\) | \(11\) |
meijerg | \(4 \,{\mathrm e}^{3} \ln \left (-4 x +1\right )\) | \(11\) |
risch | \(4 \,{\mathrm e}^{3} \ln \left (4 x -1\right )\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.38, size = 10, normalized size = 0.77 \begin {gather*} 4 \, e^{3} \log \left (4 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 8, normalized size = 0.62 \begin {gather*} 4\,\ln \left (x-\frac {1}{4}\right )\,{\mathrm {e}}^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.05, size = 10, normalized size = 0.77 \begin {gather*} 4 e^{3} \log {\left (4 x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________