3.252 \(\int \frac {1}{A+B \log (\frac {e (a+b x)}{c+d x})} \, dx\)

Optimal. Leaf size=24 \[ \text {Int}\left (\frac {1}{B \log \left (\frac {e (a+b x)}{c+d x}\right )+A},x\right ) \]

[Out]

Unintegrable(1/(A+B*ln(e*(b*x+a)/(d*x+c))),x)

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Rubi [A]  time = 0.01, 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 = {} \[ \int \frac {1}{A+B \log \left (\frac {e (a+b x)}{c+d x}\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-1),x]

[Out]

Defer[Int][(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-1), x]

Rubi steps

\begin {align*} \int \frac {1}{A+B \log \left (\frac {e (a+b x)}{c+d x}\right )} \, dx &=\int \frac {1}{A+B \log \left (\frac {e (a+b x)}{c+d x}\right )} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.02, size = 0, normalized size = 0.00 \[ \int \frac {1}{A+B \log \left (\frac {e (a+b x)}{c+d x}\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-1),x]

[Out]

Integrate[(A + B*Log[(e*(a + b*x))/(c + d*x)])^(-1), x]

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fricas [A]  time = 0.98, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{B \log \left (\frac {b e x + a e}{d x + c}\right ) + A}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm="fricas")

[Out]

integral(1/(B*log((b*e*x + a*e)/(d*x + c)) + A), x)

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm="giac")

[Out]

Timed out

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maple [A]  time = 0.92, size = 0, normalized size = 0.00 \[ \int \frac {1}{B \ln \left (\frac {\left (b x +a \right ) e}{d x +c}\right )+A}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(B*ln((b*x+a)/(d*x+c)*e)+A),x)

[Out]

int(1/(B*ln((b*x+a)/(d*x+c)*e)+A),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{B \log \left (\frac {{\left (b x + a\right )} e}{d x + c}\right ) + A}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm="maxima")

[Out]

integrate(1/(B*log((b*x + a)*e/(d*x + c)) + A), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {1}{A+B\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(A + B*log((e*(a + b*x))/(c + d*x))),x)

[Out]

int(1/(A + B*log((e*(a + b*x))/(c + d*x))), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{A + B \log {\left (\frac {e \left (a + b x\right )}{c + d x} \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(A+B*ln(e*(b*x+a)/(d*x+c))),x)

[Out]

Integral(1/(A + B*log(e*(a + b*x)/(c + d*x))), x)

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