3.65 \(\int \frac {\log (x)}{x \log (\frac {a+b x}{(b c-a d) x})} \, dx\)

Optimal. Leaf size=31 \[ \text {Int}\left (\frac {\log (x)}{x \log \left (\frac {a+b x}{x (b c-a d)}\right )},x\right ) \]

[Out]

Unintegrable(ln(x)/x/ln((b*x+a)/(-a*d+b*c)/x),x)

________________________________________________________________________________________

Rubi [A]  time = 0.02, 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 = {} \[ \int \frac {\log (x)}{x \log \left (\frac {a+b x}{(b c-a d) x}\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Log[x]/(x*Log[(a + b*x)/((b*c - a*d)*x)]),x]

[Out]

Defer[Int][Log[x]/(x*Log[(a + b*x)/((b*c - a*d)*x)]), x]

Rubi steps

\begin {align*} \int \frac {\log (x)}{x \log \left (\frac {a+b x}{(b c-a d) x}\right )} \, dx &=\int \frac {\log (x)}{x \log \left (\frac {a+b x}{(b c-a d) x}\right )} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 5.10, size = 0, normalized size = 0.00 \[ \int \frac {\log (x)}{x \log \left (\frac {a+b x}{(b c-a d) x}\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Log[x]/(x*Log[(a + b*x)/((b*c - a*d)*x)]),x]

[Out]

Integrate[Log[x]/(x*Log[(a + b*x)/((b*c - a*d)*x)]), x]

________________________________________________________________________________________

fricas [A]  time = 0.59, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \relax (x)}{x \log \left (\frac {b x + a}{{\left (b c - a d\right )} x}\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)/x/log((b*x+a)/(-a*d+b*c)/x),x, algorithm="fricas")

[Out]

integral(log(x)/(x*log((b*x + a)/((b*c - a*d)*x))), x)

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log \relax (x)}{x \log \left (\frac {b x + a}{{\left (b c - a d\right )} x}\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)/x/log((b*x+a)/(-a*d+b*c)/x),x, algorithm="giac")

[Out]

integrate(log(x)/(x*log((b*x + a)/((b*c - a*d)*x))), x)

________________________________________________________________________________________

maple [A]  time = 0.14, size = 0, normalized size = 0.00 \[ \int \frac {\ln \relax (x )}{x \ln \left (\frac {b x +a}{\left (-a d +b c \right ) x}\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(x)/x/ln((b*x+a)/(-a*d+b*c)/x),x)

[Out]

int(ln(x)/x/ln((b*x+a)/(-a*d+b*c)/x),x)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log \relax (x)}{x \log \left (\frac {b x + a}{{\left (b c - a d\right )} x}\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)/x/log((b*x+a)/(-a*d+b*c)/x),x, algorithm="maxima")

[Out]

integrate(log(x)/(x*log((b*x + a)/((b*c - a*d)*x))), x)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {\ln \relax (x)}{x\,\ln \left (-\frac {a+b\,x}{x\,\left (a\,d-b\,c\right )}\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(x)/(x*log(-(a + b*x)/(x*(a*d - b*c)))),x)

[Out]

int(log(x)/(x*log(-(a + b*x)/(x*(a*d - b*c)))), x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log {\relax (x )}}{x \log {\left (\frac {a}{- a d x + b c x} + \frac {b x}{- a d x + b c x} \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(x)/x/ln((b*x+a)/(-a*d+b*c)/x),x)

[Out]

Integral(log(x)/(x*log(a/(-a*d*x + b*c*x) + b*x/(-a*d*x + b*c*x))), x)

________________________________________________________________________________________