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

Optimal. Leaf size=30 \[ \text{Unintegrable}\left (\frac{\log (x)}{x \log \left (\frac{a+b x}{x (b c-a d)}\right )},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0216231, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., 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 = 5.0975, size = 0, normalized size = 0. \[ \int \frac{\log (x)}{x \log \left (\frac{a+b x}{(b c-a d) x}\right )} \, dx \]

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]

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Maple [A]  time = 0.089, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( x \right ) }{x} \left ( \ln \left ({\frac{bx+a}{ \left ( -ad+bc \right ) x}} \right ) \right ) ^{-1}}\, dx \end{align*}

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)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left (x\right )}{x \log \left (\frac{b x + a}{{\left (b c - a d\right )} x}\right )}\,{d x} \end{align*}

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)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\log \left (x\right )}{x \log \left (\frac{b x + a}{{\left (b c - a d\right )} x}\right )}, x\right ) \end{align*}

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)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log{\left (x \right )}}{x \log{\left (\frac{a}{- a d x + b c x} + \frac{b x}{- a d x + b c x} \right )}}\, dx \end{align*}

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)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left (x\right )}{x \log \left (\frac{b x + a}{{\left (b c - a d\right )} x}\right )}\,{d x} \end{align*}

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)