Optimal. Leaf size=35 \[ \text {Int}\left (\frac {1}{(a g+b g x) \left (A+B \log \left (\frac {e (c+d x)}{a+b x}\right )\right )^2},x\right ) \]
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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 = {}
\begin {gather*} \int \frac {1}{(a g+b g x) \left (A+B \log \left (\frac {e (c+d x)}{a+b x}\right )\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{(a g+b g x) \left (A+B \log \left (\frac {e (c+d x)}{a+b x}\right )\right )^2} \, dx &=\int \frac {1}{(a g+b g x) \left (A+B \log \left (\frac {e (c+d x)}{a+b x}\right )\right )^2} \, dx\\ \end {align*}
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Mathematica [A]
time = 0.40, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(a g+b g x) \left (A+B \log \left (\frac {e (c+d x)}{a+b x}\right )\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.61, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (b g x +a g \right ) \left (A +B \ln \left (\frac {e \left (d x +c \right )}{b x +a}\right )\right )^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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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.
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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.
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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {- c - d x}{A B a d g - A B b c g + \left (B^{2} a d g - B^{2} b c g\right ) \log {\left (\frac {e \left (c + d x\right )}{a + b x} \right )}} + \frac {d \int \frac {1}{A + B \log {\left (\frac {c e}{a + b x} + \frac {d e x}{a + b x} \right )}}\, dx}{B g \left (a d - b c\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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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.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {1}{\left (a\,g+b\,g\,x\right )\,{\left (A+B\,\ln \left (\frac {e\,\left (c+d\,x\right )}{a+b\,x}\right )\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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