Optimal. Leaf size=14 \[ \frac {4 x}{3}+4 \log (3) \log \left (x^2\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.86, number of steps
used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 45}
\begin {gather*} \frac {4 x}{3}+8 \log (3) \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {4 x+24 \log (3)}{x} \, dx\\ &=\frac {1}{3} \int \left (4+\frac {24 \log (3)}{x}\right ) \, dx\\ &=\frac {4 x}{3}+8 \log (3) \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 12, normalized size = 0.86 \begin {gather*} \frac {4 x}{3}+8 \log (3) \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.29, size = 11, normalized size = 0.79
method | result | size |
default | \(\frac {4 x}{3}+8 \ln \left (3\right ) \ln \left (x \right )\) | \(11\) |
norman | \(\frac {4 x}{3}+8 \ln \left (3\right ) \ln \left (x \right )\) | \(11\) |
risch | \(\frac {4 x}{3}+8 \ln \left (3\right ) \ln \left (x \right )\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 10, normalized size = 0.71 \begin {gather*} 8 \, \log \left (3\right ) \log \left (x\right ) + \frac {4}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 10, normalized size = 0.71 \begin {gather*} 8 \, \log \left (3\right ) \log \left (x\right ) + \frac {4}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 12, normalized size = 0.86 \begin {gather*} \frac {4 x}{3} + 8 \log {\left (3 \right )} \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 11, normalized size = 0.79 \begin {gather*} 8 \, \log \left (3\right ) \log \left ({\left | x \right |}\right ) + \frac {4}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 5.48, size = 10, normalized size = 0.71 \begin {gather*} \frac {4\,x}{3}+8\,\ln \left (3\right )\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________