Optimal. Leaf size=30 \[ \text {Int}\left (\frac {(d+e x)^m \left (a+b x+c x^2\right )^p}{f+g x},x\right ) \]
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Rubi [A] time = 0.03, 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 = {} \[ \int \frac {(d+e x)^m \left (a+b x+c x^2\right )^p}{f+g x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(d+e x)^m \left (a+b x+c x^2\right )^p}{f+g x} \, dx &=\int \frac {(d+e x)^m \left (a+b x+c x^2\right )^p}{f+g x} \, dx\\ \end {align*}
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Mathematica [A] time = 0.17, size = 0, normalized size = 0.00 \[ \int \frac {(d+e x)^m \left (a+b x+c x^2\right )^p}{f+g x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.14, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (c x^{2} + b x + a\right )}^{p} {\left (e x + d\right )}^{m}}{g x + f}, x\right ) \]
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 \[ \int \frac {{\left (c x^{2} + b x + a\right )}^{p} {\left (e x + d\right )}^{m}}{g x + f}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 0, normalized size = 0.00 \[ \int \frac {\left (e x +d \right )^{m} \left (c \,x^{2}+b x +a \right )^{p}}{g x +f}\, dx \]
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 \[ \int \frac {{\left (c x^{2} + b x + a\right )}^{p} {\left (e x + d\right )}^{m}}{g x + f}\,{d x} \]
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 \[ \int \frac {{\left (d+e\,x\right )}^m\,{\left (c\,x^2+b\,x+a\right )}^p}{f+g\,x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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