Optimal. Leaf size=30 \[ \text{Int}\left (\frac{(d+e x)^m \left (a+b x+c x^2\right )^p}{f+g x},x\right ) \]
[Out]
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Rubi [A] time = 0.0712189, 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. \[ \text{Int}\left (\frac{(d+e x)^m \left (a+b x+c x^2\right )^p}{f+g x},x\right ) \]
Verification is Not applicable to the result.
[In] Int[((d + e*x)^m*(a + b*x + c*x^2)^p)/(f + g*x),x]
[Out]
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Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (d + e x\right )^{m} \left (a + b x + c x^{2}\right )^{p}}{f + g x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)**m*(c*x**2+b*x+a)**p/(g*x+f),x)
[Out]
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Mathematica [A] time = 0.164058, size = 0, normalized size = 0. \[ \int \frac{(d+e x)^m \left (a+b x+c x^2\right )^p}{f+g x} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[((d + e*x)^m*(a + b*x + c*x^2)^p)/(f + g*x),x]
[Out]
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Maple [A] time = 0.148, size = 0, normalized size = 0. \[ \int{\frac{ \left ( ex+d \right ) ^{m} \left ( c{x}^{2}+bx+a \right ) ^{p}}{gx+f}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)^m*(c*x^2+b*x+a)^p/(g*x+f),x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (c x^{2} + b x + a\right )}^{p}{\left (e x + d\right )}^{m}}{g x + f}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^p*(e*x + d)^m/(g*x + f),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (c x^{2} + b x + a\right )}^{p}{\left (e x + d\right )}^{m}}{g x + f}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^p*(e*x + d)^m/(g*x + f),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)**m*(c*x**2+b*x+a)**p/(g*x+f),x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (c x^{2} + b x + a\right )}^{p}{\left (e x + d\right )}^{m}}{g x + f}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^p*(e*x + d)^m/(g*x + f),x, algorithm="giac")
[Out]