Optimal. Leaf size=21 \[ x-\frac {(8+x) \left (-2 x+\log \left (\frac {4}{\log (2)}\right )\right )}{x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.38, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {14}
\begin {gather*} -\frac {8 \log \left (\frac {4}{\log (2)}\right )}{x^2}+x+\frac {16-\log \left (\frac {4}{\log (2)}\right )}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {-16+\log \left (\frac {4}{\log (2)}\right )}{x^2}+\frac {16 \log \left (\frac {4}{\log (2)}\right )}{x^3}\right ) \, dx\\ &=x+\frac {16-\log \left (\frac {4}{\log (2)}\right )}{x}-\frac {8 \log \left (\frac {4}{\log (2)}\right )}{x^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 29, normalized size = 1.38 \begin {gather*} x+\frac {16-\log \left (\frac {4}{\log (2)}\right )}{x}-\frac {8 \log \left (\frac {4}{\log (2)}\right )}{x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.07, size = 29, normalized size = 1.38
method | result | size |
risch | \(x +\frac {\left (-2 \ln \left (2\right )+\ln \left (\ln \left (2\right )\right )+16\right ) x -16 \ln \left (2\right )+8 \ln \left (\ln \left (2\right )\right )}{x^{2}}\) | \(28\) |
default | \(x -\frac {8 \ln \left (\frac {4}{\ln \left (2\right )}\right )}{x^{2}}-\frac {\ln \left (\frac {4}{\ln \left (2\right )}\right )-16}{x}\) | \(29\) |
norman | \(\frac {x^{3}+\left (-2 \ln \left (2\right )+\ln \left (\ln \left (2\right )\right )+16\right ) x -16 \ln \left (2\right )+8 \ln \left (\ln \left (2\right )\right )}{x^{2}}\) | \(29\) |
gosper | \(-\frac {-x^{3}+\ln \left (\frac {4}{\ln \left (2\right )}\right ) x +8 \ln \left (\frac {4}{\ln \left (2\right )}\right )-16 x}{x^{2}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 28, normalized size = 1.33 \begin {gather*} x - \frac {x {\left (\log \left (\frac {4}{\log \left (2\right )}\right ) - 16\right )} + 8 \, \log \left (\frac {4}{\log \left (2\right )}\right )}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 23, normalized size = 1.10 \begin {gather*} \frac {x^{3} - {\left (x + 8\right )} \log \left (\frac {4}{\log \left (2\right )}\right ) + 16 \, x}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.10, size = 29, normalized size = 1.38 \begin {gather*} x + \frac {x \left (- 2 \log {\left (2 \right )} + \log {\left (\log {\left (2 \right )} \right )} + 16\right ) - 16 \log {\left (2 \right )} + 8 \log {\left (\log {\left (2 \right )} \right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 29, normalized size = 1.38 \begin {gather*} x - \frac {x \log \left (\frac {4}{\log \left (2\right )}\right ) - 16 \, x + 8 \, \log \left (\frac {4}{\log \left (2\right )}\right )}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.09, size = 26, normalized size = 1.24 \begin {gather*} x+\frac {\ln \left (\frac {{\ln \left (2\right )}^8}{65536}\right )-x\,\left (\ln \left (\frac {4}{\ln \left (2\right )}\right )-16\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________