Optimal. Leaf size=22 \[ \text{Int}\left (\frac{\sqrt{c+d x}}{\left (a+b e^x\right )^3},x\right ) \]
[Out]
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Rubi [A] time = 0.0591047, 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. \[ \text{Int}\left (\frac{\sqrt{c+d x}}{\left (a+b e^x\right )^3},x\right ) \]
Verification is Not applicable to the result.
[In] Int[Sqrt[c + d*x]/(a + b*E^x)^3,x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*x+c)**(1/2)/(a+b*exp(x))**3,x)
[Out]
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Mathematica [A] time = 1.06058, size = 0, normalized size = 0. \[ \int \frac{\sqrt{c+d x}}{\left (a+b e^x\right )^3} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[Sqrt[c + d*x]/(a + b*E^x)^3,x]
[Out]
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Maple [A] time = 0.075, size = 0, normalized size = 0. \[ \int{\frac{1}{ \left ( a+b{{\rm e}^{x}} \right ) ^{3}}\sqrt{dx+c}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*x+c)^(1/2)/(a+b*exp(x))^3,x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{d x + c}}{{\left (b e^{x} + a\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(d*x + c)/(b*e^x + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{\sqrt{d x + c}}{b^{3} e^{\left (3 \, x\right )} + 3 \, a b^{2} e^{\left (2 \, x\right )} + 3 \, a^{2} b e^{x} + a^{3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(d*x + c)/(b*e^x + a)^3,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((d*x+c)**(1/2)/(a+b*exp(x))**3,x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{d x + c}}{{\left (b e^{x} + a\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(d*x + c)/(b*e^x + a)^3,x, algorithm="giac")
[Out]