Optimal. Leaf size=31 \[ \text {Int}\left (\frac {(g+h x)^m}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )},x\right ) \]
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Rubi [A] time = 0.06, 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 = {} \[ \int \frac {(g+h x)^m}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(g+h x)^m}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx &=\int \frac {(g+h x)^m}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 0.42, size = 0, normalized size = 0.00 \[ \int \frac {(g+h x)^m}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.51, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (h x + g\right )}^{m}}{b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a}, x\right ) \]
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 \[ \int \frac {{\left (h x + g\right )}^{m}}{b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.36, size = 0, normalized size = 0.00 \[ \int \frac {\left (h x +g \right )^{m}}{b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )+a}\, dx \]
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 \[ \int \frac {{\left (h x + g\right )}^{m}}{b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a}\,{d x} \]
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 \[ \int \frac {{\left (g+h\,x\right )}^m}{a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )} \,d x \]
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 \[ \int \frac {\left (g + h x\right )^{m}}{a + b \log {\left (c \left (d \left (e + f x\right )^{p}\right )^{q} \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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