Optimal. Leaf size=37 \[ \frac{(c+d x) e^{\frac{e}{c+d x}}}{d}-\frac{e \text{ExpIntegralEi}\left (\frac{e}{c+d x}\right )}{d} \]
[Out]
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Rubi [A] time = 0.0519313, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{(c+d x) e^{\frac{e}{c+d x}}}{d}-\frac{e \text{ExpIntegralEi}\left (\frac{e}{c+d x}\right )}{d} \]
Antiderivative was successfully verified.
[In] Int[E^(e/(c + d*x)),x]
[Out]
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Rubi in Sympy [A] time = 5.85324, size = 26, normalized size = 0.7 \[ - \frac{e \operatorname{Ei}{\left (\frac{e}{c + d x} \right )}}{d} + \frac{\left (c + d x\right ) e^{\frac{e}{c + d x}}}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(e/(d*x+c)),x)
[Out]
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Mathematica [A] time = 0.0122749, size = 37, normalized size = 1. \[ \frac{(c+d x) e^{\frac{e}{c+d x}}}{d}-\frac{e \text{ExpIntegralEi}\left (\frac{e}{c+d x}\right )}{d} \]
Antiderivative was successfully verified.
[In] Integrate[E^(e/(c + d*x)),x]
[Out]
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Maple [A] time = 0.006, size = 42, normalized size = 1.1 \[ -{\frac{e}{d} \left ( -{\frac{dx+c}{e}{{\rm e}^{{\frac{e}{dx+c}}}}}-{\it Ei} \left ( 1,-{\frac{e}{dx+c}} \right ) \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(e/(d*x+c)),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ d e \int \frac{x e^{\left (\frac{e}{d x + c}\right )}}{d^{2} x^{2} + 2 \, c d x + c^{2}}\,{d x} + x e^{\left (\frac{e}{d x + c}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(e/(d*x + c)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.254495, size = 47, normalized size = 1.27 \[ -\frac{e{\rm Ei}\left (\frac{e}{d x + c}\right ) -{\left (d x + c\right )} e^{\left (\frac{e}{d x + c}\right )}}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(e/(d*x + c)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int e^{\frac{e}{c + d x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(e/(d*x+c)),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int e^{\left (\frac{e}{d x + c}\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(e/(d*x + c)),x, algorithm="giac")
[Out]