Optimal. Leaf size=114 \[ \frac {b \text {Int}\left (\frac {\log \left (1-\frac {c+d x}{a+b x}\right )}{(a+b x) \log ^2\left (\frac {a+b x}{c+d x}\right )},x\right )}{b c-a d}-\frac {d \text {Int}\left (\frac {\log \left (1-\frac {c+d x}{a+b x}\right )}{(c+d x) \log ^2\left (\frac {a+b x}{c+d x}\right )},x\right )}{b c-a d} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.35, 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 \left (1-\frac {c+d x}{a+b x}\right )}{(a+b x) (c+d x) \log ^2\left (\frac {a+b x}{c+d x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\log \left (1-\frac {c+d x}{a+b x}\right )}{(a+b x) (c+d x) \log ^2\left (\frac {a+b x}{c+d x}\right )} \, dx &=\int \left (\frac {b \log \left (1-\frac {c+d x}{a+b x}\right )}{(b c-a d) (a+b x) \log ^2\left (\frac {a+b x}{c+d x}\right )}-\frac {d \log \left (1-\frac {c+d x}{a+b x}\right )}{(b c-a d) (c+d x) \log ^2\left (\frac {a+b x}{c+d x}\right )}\right ) \, dx\\ &=\frac {b \int \frac {\log \left (1-\frac {c+d x}{a+b x}\right )}{(a+b x) \log ^2\left (\frac {a+b x}{c+d x}\right )} \, dx}{b c-a d}-\frac {d \int \frac {\log \left (1-\frac {c+d x}{a+b x}\right )}{(c+d x) \log ^2\left (\frac {a+b x}{c+d x}\right )} \, dx}{b c-a d}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.37, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log \left (1-\frac {c+d x}{a+b x}\right )}{(a+b x) (c+d x) \log ^2\left (\frac {a+b x}{c+d x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.50, size = 0, normalized size = 0.00 \[\int \frac {\ln \left (1+\frac {-d x -c}{b x +a}\right )}{\left (b x +a \right ) \left (d x +c \right ) \ln \left (\frac {b x +a}{d x +c}\right )^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
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 [A]
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(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
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 [A]
time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int \frac {\ln \left (1-\frac {c+d\,x}{a+b\,x}\right )}{{\ln \left (\frac {a+b\,x}{c+d\,x}\right )}^2\,\left (a+b\,x\right )\,\left (c+d\,x\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________