Optimal. Leaf size=31 \[ \text{Unintegrable}\left (\frac{\sqrt{a+b x+c x^2} (d+e x)^m}{f+g x},x\right ) \]
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Rubi [A] time = 0.0344326, 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 = {} \[ \int \frac{(d+e x)^m \sqrt{a+b x+c x^2}}{f+g x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{(d+e x)^m \sqrt{a+b x+c x^2}}{f+g x} \, dx &=\int \frac{(d+e x)^m \sqrt{a+b x+c x^2}}{f+g x} \, dx\\ \end{align*}
Mathematica [A] time = 0.109119, size = 0, normalized size = 0. \[ \int \frac{(d+e x)^m \sqrt{a+b x+c x^2}}{f+g x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.922, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( ex+d \right ) ^{m}}{gx+f}\sqrt{c{x}^{2}+bx+a}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{c x^{2} + b x + a}{\left (e x + d\right )}^{m}}{g x + f}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\sqrt{c x^{2} + b x + a}{\left (e x + d\right )}^{m}}{g x + f}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (d + e x\right )^{m} \sqrt{a + b x + c x^{2}}}{f + g x}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{c x^{2} + b x + a}{\left (e x + d\right )}^{m}}{g x + f}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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