Optimal. Leaf size=20 \[ -1+x+3 (-1+3 x \log (5))-x \log ^2(\log (5)) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 0.75, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {8}
\begin {gather*} x \left (1-\log ^2(\log (5))+9 \log (5)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 8
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x \left (1+9 \log (5)-\log ^2(\log (5))\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 15, normalized size = 0.75 \begin {gather*} x+9 x \log (5)-x \log ^2(\log (5)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.11, size = 16, normalized size = 0.80
method | result | size |
default | \(x \left (-\ln \left (\ln \left (5\right )\right )^{2}+9 \ln \left (5\right )+1\right )\) | \(16\) |
norman | \(x \left (-\ln \left (\ln \left (5\right )\right )^{2}+9 \ln \left (5\right )+1\right )\) | \(16\) |
risch | \(-x \ln \left (\ln \left (5\right )\right )^{2}+9 x \ln \left (5\right )+x\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 14, normalized size = 0.70 \begin {gather*} -{\left (\log \left (\log \left (5\right )\right )^{2} - 9 \, \log \left (5\right ) - 1\right )} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.44, size = 15, normalized size = 0.75 \begin {gather*} -x \log \left (\log \left (5\right )\right )^{2} + 9 \, x \log \left (5\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 14, normalized size = 0.70 \begin {gather*} x \left (- \log {\left (\log {\left (5 \right )} \right )}^{2} + 1 + 9 \log {\left (5 \right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.38, size = 14, normalized size = 0.70 \begin {gather*} -{\left (\log \left (\log \left (5\right )\right )^{2} - 9 \, \log \left (5\right ) - 1\right )} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.00, size = 15, normalized size = 0.75 \begin {gather*} x\,\left (9\,\ln \left (5\right )-{\ln \left (\ln \left (5\right )\right )}^2+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________