Optimal. Leaf size=38 \[ \text {Int}\left (\frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )},x\right ) \]
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Rubi [A] time = 0.30, 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 = {} \[ \int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{(g+h x) (542+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx &=\int \frac {1}{(g+h x) (542+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 1.07, size = 0, normalized size = 0.00 \[ \int \frac {1}{(g+h x) (i+j x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a h j x^{2} + a g i + {\left (a h i + a g j\right )} x + {\left (b h j x^{2} + b g i + {\left (b h i + b g j\right )} x\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )}, x\right ) \]
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 \[ \int \frac {1}{{\left (h x + g\right )} {\left (j x + i\right )} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.54, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (h x +g \right ) \left (j x +i \right ) \left (b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )+a \right )}\, dx \]
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 \[ \int \frac {1}{{\left (h x + g\right )} {\left (j x + i\right )} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}}\,{d x} \]
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 \[ \int \frac {1}{\left (g+h\,x\right )\,\left (i+j\,x\right )\,\left (a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )\right )} \,d x \]
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 \[ \int \frac {1}{\left (a + b \log {\left (c \left (d \left (e + f x\right )^{p}\right )^{q} \right )}\right ) \left (g + h x\right ) \left (i + j x\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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