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

Optimal. Leaf size=34 \[ \text{Unintegrable}\left (\frac{1}{(a g+b g x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )},x\right ) \]

[Out]

Unintegrable[1/((a*g + b*g*x)*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]

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Rubi [A]  time = 0.0718844, 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 = {} \[ \int \frac{1}{(a g+b g x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.225396, size = 0, normalized size = 0. \[ \int \frac{1}{(a g+b g x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 1.183, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{bgx+ag} \left ( A+B\ln \left ({\frac{e \left ( bx+a \right ) }{dx+c}} \right ) \right ) ^{-1}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b g x + a g\right )}{\left (B \log \left (\frac{{\left (b x + a\right )} e}{d x + c}\right ) + A\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{A b g x + A a g +{\left (B b g x + B a g\right )} \log \left (\frac{b e x + a e}{d x + c}\right )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b g x + a g\right )}{\left (B \log \left (\frac{{\left (b x + a\right )} e}{d x + c}\right ) + A\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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