Optimal. Leaf size=519 \[ \frac {1}{12} \left (\log ^4\left (-\frac {b x}{a}\right )+6 \log ^2\left (-\frac {b x}{a}\right ) \log ^2\left (-\frac {b x}{a+b x}\right )-4 \left (\log \left (-\frac {b x}{a}\right )+\log \left (\frac {a}{a+b x}\right )\right ) \log ^3\left (-\frac {b x}{a+b x}\right )+\log ^4\left (-\frac {b x}{a+b x}\right )+6 \log ^2(x) \log ^2(a+b x)+4 \left (2 \log ^3\left (-\frac {b x}{a}\right )-3 \log ^2(x) \log (a+b x)\right ) \log \left (1+\frac {b x}{a}\right )+6 \left (\log (x)-\log \left (-\frac {b x}{a}\right )\right ) \left (\log (x)+3 \log \left (-\frac {b x}{a}\right )\right ) \log ^2\left (1+\frac {b x}{a}\right )-4 \log ^2\left (-\frac {b x}{a}\right ) \log \left (-\frac {b x}{a+b x}\right ) \left (\log \left (-\frac {b x}{a}\right )+3 \log \left (1+\frac {b x}{a}\right )\right )+12 \left (\log ^2\left (-\frac {b x}{a}\right )-2 \log \left (-\frac {b x}{a}\right ) \left (\log \left (-\frac {b x}{a+b x}\right )+\log \left (1+\frac {b x}{a}\right )\right )+2 \log (x) \left (-\log (a+b x)+\log \left (1+\frac {b x}{a}\right )\right )\right ) \text {Li}_2\left (-\frac {b x}{a}\right )-12 \log ^2\left (-\frac {b x}{a+b x}\right ) \text {Li}_2\left (\frac {b x}{a+b x}\right )+12 \left (\log \left (-\frac {b x}{a}\right )-\log \left (-\frac {b x}{a+b x}\right )\right )^2 \text {Li}_2\left (1+\frac {b x}{a}\right )+24 \left (\log (x)-\log \left (-\frac {b x}{a}\right )\right ) \log \left (1+\frac {b x}{a}\right ) \text {Li}_2\left (1+\frac {b x}{a}\right )+24 \left (\log \left (-\frac {b x}{a+b x}\right )+\log (a+b x)\right ) \text {Li}_3\left (-\frac {b x}{a}\right )+24 \log \left (-\frac {b x}{a+b x}\right ) \text {Li}_3\left (\frac {b x}{a+b x}\right )+24 \left (-\log (x)+\log \left (-\frac {b x}{a+b x}\right )\right ) \text {Li}_3\left (1+\frac {b x}{a}\right )-24 \left (\text {Li}_4\left (-\frac {b x}{a}\right )+\text {Li}_4\left (\frac {b x}{a+b x}\right )-\text {Li}_4\left (1+\frac {b x}{a}\right )\right )\right ) \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 0.03, 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 {\log (x) \log ^2(a+b x)}{x} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\log (x) \log ^2(a+b x)}{x} \, dx &=\frac {1}{2} \log ^2(x) \log ^2(a+b x)-b \int \frac {\log ^2(x) \log (a+b x)}{a+b x} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.07, size = 519, normalized size = 1.00 \begin {gather*} \frac {1}{12} \left (\log ^4\left (-\frac {b x}{a}\right )+6 \log ^2\left (-\frac {b x}{a}\right ) \log ^2\left (-\frac {b x}{a+b x}\right )-4 \left (\log \left (-\frac {b x}{a}\right )+\log \left (\frac {a}{a+b x}\right )\right ) \log ^3\left (-\frac {b x}{a+b x}\right )+\log ^4\left (-\frac {b x}{a+b x}\right )+6 \log ^2(x) \log ^2(a+b x)+4 \left (2 \log ^3\left (-\frac {b x}{a}\right )-3 \log ^2(x) \log (a+b x)\right ) \log \left (1+\frac {b x}{a}\right )+6 \left (\log (x)-\log \left (-\frac {b x}{a}\right )\right ) \left (\log (x)+3 \log \left (-\frac {b x}{a}\right )\right ) \log ^2\left (1+\frac {b x}{a}\right )-4 \log ^2\left (-\frac {b x}{a}\right ) \log \left (-\frac {b x}{a+b x}\right ) \left (\log \left (-\frac {b x}{a}\right )+3 \log \left (1+\frac {b x}{a}\right )\right )+12 \left (\log ^2\left (-\frac {b x}{a}\right )-2 \log \left (-\frac {b x}{a}\right ) \left (\log \left (-\frac {b x}{a+b x}\right )+\log \left (1+\frac {b x}{a}\right )\right )+2 \log (x) \left (-\log (a+b x)+\log \left (1+\frac {b x}{a}\right )\right )\right ) \text {Li}_2\left (-\frac {b x}{a}\right )-12 \log ^2\left (-\frac {b x}{a+b x}\right ) \text {Li}_2\left (\frac {b x}{a+b x}\right )+12 \left (\log \left (-\frac {b x}{a}\right )-\log \left (-\frac {b x}{a+b x}\right )\right )^2 \text {Li}_2\left (1+\frac {b x}{a}\right )+24 \left (\log (x)-\log \left (-\frac {b x}{a}\right )\right ) \log \left (1+\frac {b x}{a}\right ) \text {Li}_2\left (1+\frac {b x}{a}\right )+24 \left (\log \left (-\frac {b x}{a+b x}\right )+\log (a+b x)\right ) \text {Li}_3\left (-\frac {b x}{a}\right )+24 \log \left (-\frac {b x}{a+b x}\right ) \text {Li}_3\left (\frac {b x}{a+b x}\right )+24 \left (-\log (x)+\log \left (-\frac {b x}{a+b x}\right )\right ) \text {Li}_3\left (1+\frac {b x}{a}\right )-24 \left (\text {Li}_4\left (-\frac {b x}{a}\right )+\text {Li}_4\left (\frac {b x}{a+b x}\right )-\text {Li}_4\left (1+\frac {b x}{a}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F]
time = 0.31, size = 0, normalized size = 0.00 \[\int \frac {\ln \left (x \right ) \ln \left (b x +a \right )^{2}}{x}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} - b \int \frac {\log {\left (x \right )}^{2} \log {\left (a + b x \right )}}{a + b x}\, dx + \frac {\log {\left (x \right )}^{2} \log {\left (a + b x \right )}^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {{\ln \left (a+b\,x\right )}^2\,\ln \left (x\right )}{x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________