Optimal. Leaf size=20 \[ \frac {1}{-x+\log \left (\log \left (\frac {2}{\log \left (5+\frac {47 x}{2}\right )}\right )\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.10, antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps
used = 2, number of rules used = 2, integrand size = 174, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {6820, 6818}
\begin {gather*} -\frac {1}{x-\log \left (\log \left (\frac {2}{\log \left (\frac {47 x}{2}+5\right )}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1+\frac {47}{(10+47 x) \log \left (5+\frac {47 x}{2}\right ) \log \left (\frac {2}{\log \left (5+\frac {47 x}{2}\right )}\right )}}{\left (x-\log \left (\log \left (\frac {2}{\log \left (5+\frac {47 x}{2}\right )}\right )\right )\right )^2} \, dx\\ &=-\frac {1}{x-\log \left (\log \left (\frac {2}{\log \left (5+\frac {47 x}{2}\right )}\right )\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 22, normalized size = 1.10 \begin {gather*} -\frac {1}{x-\log \left (\log \left (\frac {2}{\log \left (5+\frac {47 x}{2}\right )}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 60.39, size = 22, normalized size = 1.10
method | result | size |
risch | \(-\frac {1}{x -\ln \left (\ln \left (2\right )-\ln \left (\ln \left (\frac {47 x}{2}+5\right )\right )\right )}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.56, size = 26, normalized size = 1.30 \begin {gather*} -\frac {1}{x - \log \left (\log \left (2\right ) - \log \left (-\log \left (2\right ) + \log \left (47 \, x + 10\right )\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.34, size = 20, normalized size = 1.00 \begin {gather*} -\frac {1}{x - \log \left (\log \left (\frac {2}{\log \left (\frac {47}{2} \, x + 5\right )}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.15, size = 15, normalized size = 0.75 \begin {gather*} \frac {1}{- x + \log {\left (\log {\left (\frac {2}{\log {\left (\frac {47 x}{2} + 5 \right )}} \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 590 vs.
\(2 (20) = 40\).
time = 2.60, size = 590, normalized size = 29.50 \begin {gather*} -\frac {47 \, x \log \left (2\right )^{2} \log \left (\frac {47}{2} \, x + 5\right ) - 47 \, x \log \left (2\right ) \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) - 47 \, x \log \left (2\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) + 47 \, x \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) + 10 \, \log \left (2\right )^{2} \log \left (\frac {47}{2} \, x + 5\right ) - 10 \, \log \left (2\right ) \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) - 10 \, \log \left (2\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) + 10 \, \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) - 47 \, \log \left (\frac {47}{2} \, x + 5\right )}{47 \, x^{2} \log \left (2\right )^{2} \log \left (\frac {47}{2} \, x + 5\right ) - 47 \, x^{2} \log \left (2\right ) \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) - 47 \, x \log \left (2\right )^{2} \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (2\right ) - \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right )\right ) + 47 \, x \log \left (2\right ) \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (2\right ) - \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right )\right ) - 47 \, x^{2} \log \left (2\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) + 47 \, x^{2} \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) + 47 \, x \log \left (2\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (2\right ) - \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right )\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) - 47 \, x \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (2\right ) - \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right )\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) + 10 \, x \log \left (2\right )^{2} \log \left (\frac {47}{2} \, x + 5\right ) - 10 \, x \log \left (2\right ) \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) - 10 \, \log \left (2\right )^{2} \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (2\right ) - \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right )\right ) + 10 \, \log \left (2\right ) \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (2\right ) - \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right )\right ) - 10 \, x \log \left (2\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) + 10 \, x \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) + 10 \, \log \left (2\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (2\right ) - \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right )\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) - 10 \, \log \left (47 \, x + 10\right ) \log \left (\frac {47}{2} \, x + 5\right ) \log \left (\log \left (2\right ) - \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right )\right ) \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right ) + 47 \, x \log \left (2\right ) - 47 \, x \log \left (47 \, x + 10\right ) - 47 \, \log \left (2\right ) \log \left (\log \left (2\right ) - \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right )\right ) + 47 \, \log \left (47 \, x + 10\right ) \log \left (\log \left (2\right ) - \log \left (\log \left (\frac {47}{2} \, x + 5\right )\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 5.01, size = 20, normalized size = 1.00 \begin {gather*} -\frac {1}{x-\ln \left (\ln \left (\frac {2}{\ln \left (\frac {47\,x}{2}+5\right )}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________