Optimal. Leaf size=14 \[ -4+\frac {9}{\log \left (-3+e^5+\log (x)\right )} \]
________________________________________________________________________________________
Rubi [A] time = 0.06, antiderivative size = 12, normalized size of antiderivative = 0.86, number of steps used = 6, number of rules used = 5, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.185, Rules used = {6, 12, 2390, 2302, 30} \begin {gather*} \frac {9}{\log \left (\log (x)+e^5-3\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 12
Rule 30
Rule 2302
Rule 2390
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int -\frac {9}{\left (\left (-3+e^5\right ) x+x \log (x)\right ) \log ^2\left (-3+e^5+\log (x)\right )} \, dx\\ &=-\left (9 \int \frac {1}{\left (\left (-3+e^5\right ) x+x \log (x)\right ) \log ^2\left (-3+e^5+\log (x)\right )} \, dx\right )\\ &=-\left (9 \operatorname {Subst}\left (\int \frac {1}{\left (-3+e^5+x\right ) \log ^2\left (-3+e^5+x\right )} \, dx,x,\log (x)\right )\right )\\ &=-\left (9 \operatorname {Subst}\left (\int \frac {1}{x \log ^2(x)} \, dx,x,-3+e^5+\log (x)\right )\right )\\ &=-\left (9 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log \left (-3+e^5+\log (x)\right )\right )\right )\\ &=\frac {9}{\log \left (-3+e^5+\log (x)\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 12, normalized size = 0.86 \begin {gather*} \frac {9}{\log \left (-3+e^5+\log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.77, size = 11, normalized size = 0.79 \begin {gather*} \frac {9}{\log \left (e^{5} + \log \relax (x) - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.13, size = 11, normalized size = 0.79 \begin {gather*} \frac {9}{\log \left (e^{5} + \log \relax (x) - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.10, size = 12, normalized size = 0.86
method | result | size |
default | \(\frac {9}{\ln \left (\ln \relax (x )+{\mathrm e}^{5}-3\right )}\) | \(12\) |
norman | \(\frac {9}{\ln \left (\ln \relax (x )+{\mathrm e}^{5}-3\right )}\) | \(12\) |
risch | \(\frac {9}{\ln \left (\ln \relax (x )+{\mathrm e}^{5}-3\right )}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 11, normalized size = 0.79 \begin {gather*} \frac {9}{\log \left (e^{5} + \log \relax (x) - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 5.58, size = 11, normalized size = 0.79 \begin {gather*} \frac {9}{\ln \left ({\mathrm {e}}^5+\ln \relax (x)-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.26, size = 10, normalized size = 0.71 \begin {gather*} \frac {9}{\log {\left (\log {\relax (x )} - 3 + e^{5} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________