Optimal. Leaf size=22 \[ \text{Int}\left (\frac{e^{\frac{e}{(c+d x)^2}}}{a+b x},x\right ) \]
[Out]
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Rubi [A] time = 0.0372409, 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. \[ \text{Int}\left (\frac{e^{\frac{e}{(c+d x)^2}}}{a+b x},x\right ) \]
Verification is Not applicable to the result.
[In] Int[E^(e/(c + d*x)^2)/(a + b*x),x]
[Out]
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Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\frac{e}{\left (c + d x\right )^{2}}}}{a + b x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(e/(d*x+c)**2)/(b*x+a),x)
[Out]
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Mathematica [A] time = 0.0335861, size = 0, normalized size = 0. \[ \int \frac{e^{\frac{e}{(c+d x)^2}}}{a+b x} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[E^(e/(c + d*x)^2)/(a + b*x),x]
[Out]
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Maple [A] time = 0.072, size = 0, normalized size = 0. \[ \int{\frac{1}{bx+a}{{\rm e}^{{\frac{e}{ \left ( dx+c \right ) ^{2}}}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(e/(d*x+c)^2)/(b*x+a),x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\left (\frac{e}{{\left (d x + c\right )}^{2}}\right )}}{b x + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(e/(d*x + c)^2)/(b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{e^{\left (\frac{e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right )}}{b x + a}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(e/(d*x + c)^2)/(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\frac{e}{c^{2} + 2 c d x + d^{2} x^{2}}}}{a + b x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(e/(d*x+c)**2)/(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\left (\frac{e}{{\left (d x + c\right )}^{2}}\right )}}{b x + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(e/(d*x + c)^2)/(b*x + a),x, algorithm="giac")
[Out]