Optimal. Leaf size=23 \[ \frac {1}{5} (-1-x-x (2+x \log (3))) \log (\log (6+x)) \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 0.27, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-1-3 x-x^2 \log (3)+\left (-18-3 x+\left (-12 x-2 x^2\right ) \log (3)\right ) \log (6+x) \log (\log (6+x))}{(30+5 x) \log (6+x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-1-3 x-x^2 \log (3)}{5 (6+x) \log (6+x)}-\frac {1}{5} (3+x \log (9)) \log (\log (6+x))\right ) \, dx\\ &=\frac {1}{5} \int \frac {-1-3 x-x^2 \log (3)}{(6+x) \log (6+x)} \, dx-\frac {1}{5} \int (3+x \log (9)) \log (\log (6+x)) \, dx\\ &=\frac {1}{5} \int \left (\frac {17-36 \log (3)}{(6+x) \log (6+x)}-\frac {x \log (3)}{\log (6+x)}-\frac {3 (1-\log (9))}{\log (6+x)}\right ) \, dx-\frac {1}{5} \int (3 \log (\log (6+x))+x \log (9) \log (\log (6+x))) \, dx\\ &=-\left (\frac {3}{5} \int \log (\log (6+x)) \, dx\right )+\frac {1}{5} (17-36 \log (3)) \int \frac {1}{(6+x) \log (6+x)} \, dx-\frac {1}{5} \log (3) \int \frac {x}{\log (6+x)} \, dx-\frac {1}{5} (3 (1-\log (9))) \int \frac {1}{\log (6+x)} \, dx-\frac {1}{5} \log (9) \int x \log (\log (6+x)) \, dx\\ &=-\left (\frac {3}{5} \text {Subst}(\int \log (\log (x)) \, dx,x,6+x)\right )+\frac {1}{5} (17-36 \log (3)) \text {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,6+x\right )-\frac {1}{5} \log (3) \int \left (-\frac {6}{\log (6+x)}+\frac {6+x}{\log (6+x)}\right ) \, dx-\frac {1}{5} (3 (1-\log (9))) \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,6+x\right )-\frac {1}{5} \log (9) \int x \log (\log (6+x)) \, dx\\ &=-\frac {3}{5} (6+x) \log (\log (6+x))-\frac {3}{5} (1-\log (9)) \text {li}(6+x)+\frac {3}{5} \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,6+x\right )+\frac {1}{5} (17-36 \log (3)) \text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (6+x)\right )-\frac {1}{5} \log (3) \int \frac {6+x}{\log (6+x)} \, dx+\frac {1}{5} (6 \log (3)) \int \frac {1}{\log (6+x)} \, dx-\frac {1}{5} \log (9) \int x \log (\log (6+x)) \, dx\\ &=-\frac {3}{5} (6+x) \log (\log (6+x))+\frac {1}{5} (17-36 \log (3)) \log (\log (6+x))+\frac {3 \text {li}(6+x)}{5}-\frac {3}{5} (1-\log (9)) \text {li}(6+x)-\frac {1}{5} \log (3) \text {Subst}\left (\int \frac {x}{\log (x)} \, dx,x,6+x\right )+\frac {1}{5} (6 \log (3)) \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,6+x\right )-\frac {1}{5} \log (9) \int x \log (\log (6+x)) \, dx\\ &=-\frac {3}{5} (6+x) \log (\log (6+x))+\frac {1}{5} (17-36 \log (3)) \log (\log (6+x))+\frac {3 \text {li}(6+x)}{5}+\frac {6}{5} \log (3) \text {li}(6+x)-\frac {3}{5} (1-\log (9)) \text {li}(6+x)-\frac {1}{5} \log (3) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (6+x)\right )-\frac {1}{5} \log (9) \int x \log (\log (6+x)) \, dx\\ &=-\frac {1}{5} \text {Ei}(2 \log (6+x)) \log (3)-\frac {3}{5} (6+x) \log (\log (6+x))+\frac {1}{5} (17-36 \log (3)) \log (\log (6+x))+\frac {3 \text {li}(6+x)}{5}+\frac {6}{5} \log (3) \text {li}(6+x)-\frac {3}{5} (1-\log (9)) \text {li}(6+x)-\frac {1}{5} \log (9) \int x \log (\log (6+x)) \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.09, size = 20, normalized size = 0.87 \begin {gather*} -\frac {1}{5} \left (1+3 x+x^2 \log (3)\right ) \log (\log (6+x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.38, size = 29, normalized size = 1.26
method | result | size |
risch | \(\left (-\frac {x^{2} \ln \left (3\right )}{5}-\frac {3 x}{5}\right ) \ln \left (\ln \left (x +6\right )\right )-\frac {\ln \left (\ln \left (x +6\right )\right )}{5}\) | \(26\) |
default | \(-\frac {\ln \left (3\right ) \ln \left (\ln \left (x +6\right )\right ) x^{2}}{5}-\frac {\ln \left (\ln \left (x +6\right )\right )}{5}-\frac {3 x \ln \left (\ln \left (x +6\right )\right )}{5}\) | \(29\) |
norman | \(-\frac {\ln \left (3\right ) \ln \left (\ln \left (x +6\right )\right ) x^{2}}{5}-\frac {\ln \left (\ln \left (x +6\right )\right )}{5}-\frac {3 x \ln \left (\ln \left (x +6\right )\right )}{5}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.52, size = 25, normalized size = 1.09 \begin {gather*} -\frac {1}{5} \, {\left (x^{2} \log \left (3\right ) + 3 \, x\right )} \log \left (\log \left (x + 6\right )\right ) - \frac {1}{5} \, \log \left (\log \left (x + 6\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.31, size = 18, normalized size = 0.78 \begin {gather*} -\frac {1}{5} \, {\left (x^{2} \log \left (3\right ) + 3 \, x + 1\right )} \log \left (\log \left (x + 6\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.32, size = 46, normalized size = 2.00 \begin {gather*} \left (- \frac {x^{2} \log {\left (3 \right )}}{5} - \frac {3 x}{5} - \frac {9}{5} + \frac {12 \log {\left (3 \right )}}{5}\right ) \log {\left (\log {\left (x + 6 \right )} \right )} - \frac {4 \left (-2 + 3 \log {\left (3 \right )}\right ) \log {\left (\log {\left (x + 6 \right )} \right )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 25, normalized size = 1.09 \begin {gather*} -\frac {1}{5} \, {\left (x^{2} \log \left (3\right ) + 3 \, x\right )} \log \left (\log \left (x + 6\right )\right ) - \frac {1}{5} \, \log \left (\log \left (x + 6\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.83, size = 18, normalized size = 0.78 \begin {gather*} -\frac {\ln \left (\ln \left (x+6\right )\right )\,\left (\ln \left (3\right )\,x^2+3\,x+1\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________