Optimal. Leaf size=32 \[ \text{Int}\left (\frac{(d+e x)^m}{(f+g x) \sqrt{a+b x+c x^2}},x\right ) \]
[Out]
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Rubi [A] time = 0.125835, 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. \[ \text{Int}\left (\frac{(d+e x)^m}{(f+g x) \sqrt{a+b x+c x^2}},x\right ) \]
Verification is Not applicable to the result.
[In] Int[(d + e*x)^m/((f + g*x)*Sqrt[a + b*x + c*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (d + e x\right )^{m}}{\left (f + g x\right ) \sqrt{a + b x + c x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)**m/(g*x+f)/(c*x**2+b*x+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.101683, size = 0, normalized size = 0. \[ \int \frac{(d+e x)^m}{(f+g x) \sqrt{a+b x+c x^2}} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(d + e*x)^m/((f + g*x)*Sqrt[a + b*x + c*x^2]),x]
[Out]
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Maple [A] time = 0.125, size = 0, normalized size = 0. \[ \int{\frac{ \left ( ex+d \right ) ^{m}}{gx+f}{\frac{1}{\sqrt{c{x}^{2}+bx+a}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)^m/(g*x+f)/(c*x^2+b*x+a)^(1/2),x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (e x + d\right )}^{m}}{\sqrt{c x^{2} + b x + a}{\left (g x + f\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^m/(sqrt(c*x^2 + b*x + a)*(g*x + f)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (e x + d\right )}^{m}}{\sqrt{c x^{2} + b x + a}{\left (g x + f\right )}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^m/(sqrt(c*x^2 + b*x + a)*(g*x + f)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (d + e x\right )^{m}}{\left (f + g x\right ) \sqrt{a + b x + c x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)**m/(g*x+f)/(c*x**2+b*x+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (e x + d\right )}^{m}}{\sqrt{c x^{2} + b x + a}{\left (g x + f\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^m/(sqrt(c*x^2 + b*x + a)*(g*x + f)),x, algorithm="giac")
[Out]