Optimal. Leaf size=32 \[ \text {Int}\left (\frac {(d+e x)^m}{(f+g x) \sqrt {a+b x+c x^2}},x\right ) \]
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Rubi [A] time = 0.04, 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 = {} \[ \int \frac {(d+e x)^m}{(f+g x) \sqrt {a+b x+c x^2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(d+e x)^m}{(f+g x) \sqrt {a+b x+c x^2}} \, dx &=\int \frac {(d+e x)^m}{(f+g x) \sqrt {a+b x+c x^2}} \, dx\\ \end {align*}
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Mathematica [A] time = 0.12, size = 0, normalized size = 0.00 \[ \int \frac {(d+e x)^m}{(f+g x) \sqrt {a+b x+c x^2}} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.08, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {c x^{2} + b x + a} {\left (e x + d\right )}^{m}}{c g x^{3} + {\left (c f + b g\right )} x^{2} + a f + {\left (b f + a g\right )} x}, x\right ) \]
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 \[ \int \frac {{\left (e x + d\right )}^{m}}{\sqrt {c x^{2} + b x + a} {\left (g x + f\right )}}\,{d x} \]
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 \[ \int \frac {\left (e x +d \right )^{m}}{\left (g x +f \right ) \sqrt {c \,x^{2}+b x +a}}\, dx \]
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 \[ \int \frac {{\left (e x + d\right )}^{m}}{\sqrt {c x^{2} + b x + a} {\left (g x + f\right )}}\,{d x} \]
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 \[ \int \frac {{\left (d+e\,x\right )}^m}{\left (f+g\,x\right )\,\sqrt {c\,x^2+b\,x+a}} \,d x \]
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 \[ \int \frac {\left (d + e x\right )^{m}}{\left (f + g x\right ) \sqrt {a + b x + c x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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