Optimal. Leaf size=20 \[ \text{Int}\left (\frac{1}{x \left (a+b e^{c+d x}\right )},x\right ) \]
[Out]
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Rubi [A] time = 0.0741346, 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. \[ \text{Int}\left (\frac{1}{\left (a+b e^{c+d x}\right ) x},x\right ) \]
Verification is Not applicable to the result.
[In] Int[1/((a + b*E^(c + d*x))*x),x]
[Out]
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Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{x \left (a + b e^{c + d x}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b*exp(d*x+c))/x,x)
[Out]
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Mathematica [A] time = 0.104162, size = 0, normalized size = 0. \[ \int \frac{1}{\left (a+b e^{c+d x}\right ) x} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[1/((a + b*E^(c + d*x))*x),x]
[Out]
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Maple [A] time = 0.017, size = 0, normalized size = 0. \[ \int{\frac{1}{ \left ( a+b{{\rm e}^{dx+c}} \right ) x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b*exp(d*x+c))/x,x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b e^{\left (d x + c\right )} + a\right )} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*e^(d*x + c) + a)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{b x e^{\left (d x + c\right )} + a x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*e^(d*x + c) + a)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{x \left (a + b e^{c} e^{d x}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b*exp(d*x+c))/x,x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b e^{\left (d x + c\right )} + a\right )} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*e^(d*x + c) + a)*x),x, algorithm="giac")
[Out]