Optimal. Leaf size=15 \[ x^2+\log \left (-\frac {49}{4}+\log \left (\frac {x}{4}\right )\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.39, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 7, number of rules used = 6, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {2641, 6873, 12,
6874, 2339, 29} \begin {gather*} x^2+\log \left (49-4 \log \left (\frac {x}{4}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 29
Rule 2339
Rule 2641
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4-98 x^2+8 x^2 \log \left (\frac {x}{4}\right )}{x \left (-49+4 \log \left (\frac {x}{4}\right )\right )} \, dx\\ &=\int \frac {2 \left (-2+49 x^2-4 x^2 \log \left (\frac {x}{4}\right )\right )}{x \left (49-4 \log \left (\frac {x}{4}\right )\right )} \, dx\\ &=2 \int \frac {-2+49 x^2-4 x^2 \log \left (\frac {x}{4}\right )}{x \left (49-4 \log \left (\frac {x}{4}\right )\right )} \, dx\\ &=2 \int \left (x+\frac {2}{x \left (-49+4 \log \left (\frac {x}{4}\right )\right )}\right ) \, dx\\ &=x^2+4 \int \frac {1}{x \left (-49+4 \log \left (\frac {x}{4}\right )\right )} \, dx\\ &=x^2+\text {Subst}\left (\int \frac {1}{x} \, dx,x,-49+4 \log \left (\frac {x}{4}\right )\right )\\ &=x^2+\log \left (49-4 \log \left (\frac {x}{4}\right )\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.05, size = 15, normalized size = 1.00 \begin {gather*} x^2+\log \left (49-4 \log \left (\frac {x}{4}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.95, size = 14, normalized size = 0.93
method | result | size |
risch | \(x^{2}+\ln \left (\ln \left (\frac {x}{4}\right )-\frac {49}{4}\right )\) | \(12\) |
derivativedivides | \(\ln \left (4 \ln \left (\frac {x}{4}\right )-49\right )+x^{2}\) | \(14\) |
default | \(\ln \left (4 \ln \left (\frac {x}{4}\right )-49\right )+x^{2}\) | \(14\) |
norman | \(\ln \left (4 \ln \left (\frac {x}{4}\right )-49\right )+x^{2}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.51, size = 13, normalized size = 0.87 \begin {gather*} x^{2} + \log \left (-2 \, \log \left (2\right ) + \log \left (x\right ) - \frac {49}{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.39, size = 13, normalized size = 0.87 \begin {gather*} x^{2} + \log \left (4 \, \log \left (\frac {1}{4} \, x\right ) - 49\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 12, normalized size = 0.80 \begin {gather*} x^{2} + \log {\left (\log {\left (\frac {x}{4} \right )} - \frac {49}{4} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 13, normalized size = 0.87 \begin {gather*} x^{2} + \log \left (4 \, \log \left (\frac {1}{4} \, x\right ) - 49\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.37, size = 13, normalized size = 0.87 \begin {gather*} \ln \left (4\,\ln \left (\frac {x}{4}\right )-49\right )+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________