Optimal. Leaf size=153 \[ \frac{3 d e (b c-a d)^2 \text{Int}\left (\frac{e^{e (c+d x)^3}}{a+b x},x\right )}{b^3}-\frac{d e (c+d x) (b c-a d) \text{Gamma}\left (\frac{1}{3},-e (c+d x)^3\right )}{b^3 \sqrt [3]{-e (c+d x)^3}}-\frac{d e (c+d x)^2 \text{Gamma}\left (\frac{2}{3},-e (c+d x)^3\right )}{b^2 \left (-e (c+d x)^3\right )^{2/3}}-\frac{e^{e (c+d x)^3}}{b (a+b x)} \]
[Out]
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Rubi [A] time = 0.548302, 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. \[ \text{Int}\left (\frac{e^{e (c+d x)^3}}{(a+b x)^2},x\right ) \]
Verification is Not applicable to the result.
[In] Int[E^(e*(c + d*x)^3)/(a + b*x)^2,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(exp(e*(d*x+c)**3)/(b*x+a)**2,x)
[Out]
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Mathematica [A] time = 3.09781, size = 0, normalized size = 0. \[ \int \frac{e^{e (c+d x)^3}}{(a+b x)^2} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[E^(e*(c + d*x)^3)/(a + b*x)^2,x]
[Out]
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Maple [A] time = 0.053, size = 0, normalized size = 0. \[ \int{\frac{{{\rm e}^{e \left ( dx+c \right ) ^{3}}}}{ \left ( bx+a \right ) ^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(e*(d*x+c)^3)/(b*x+a)^2,x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\left ({\left (d x + c\right )}^{3} e\right )}}{{\left (b x + a\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^((d*x + c)^3*e)/(b*x + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{e^{\left (d^{3} e x^{3} + 3 \, c d^{2} e x^{2} + 3 \, c^{2} d e x + c^{3} e\right )}}{b^{2} x^{2} + 2 \, a b x + a^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^((d*x + c)^3*e)/(b*x + a)^2,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(exp(e*(d*x+c)**3)/(b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \mathit{undef} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^((d*x + c)^3*e)/(b*x + a)^2,x, algorithm="giac")
[Out]