Optimal. Leaf size=92 \[ \frac{(c+d x) (b c-a d) \text{Gamma}\left (\frac{1}{3},-e (c+d x)^3\right )}{3 d^2 \sqrt [3]{-e (c+d x)^3}}-\frac{b (c+d x)^2 \text{Gamma}\left (\frac{2}{3},-e (c+d x)^3\right )}{3 d^2 \left (-e (c+d x)^3\right )^{2/3}} \]
[Out]
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Rubi [A] time = 0.109915, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ \frac{(c+d x) (b c-a d) \text{Gamma}\left (\frac{1}{3},-e (c+d x)^3\right )}{3 d^2 \sqrt [3]{-e (c+d x)^3}}-\frac{b (c+d x)^2 \text{Gamma}\left (\frac{2}{3},-e (c+d x)^3\right )}{3 d^2 \left (-e (c+d x)^3\right )^{2/3}} \]
Antiderivative was successfully verified.
[In] Int[E^(e*(c + d*x)^3)*(a + b*x),x]
[Out]
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Rubi in Sympy [A] time = 11.2215, size = 85, normalized size = 0.92 \[ - \frac{b \left (c + d x\right )^{2} \Gamma{\left (\frac{2}{3},- e \left (c + d x\right )^{3} \right )}}{3 d^{2} \left (- e \left (c + d x\right )^{3}\right )^{\frac{2}{3}}} - \frac{\left (c + d x\right ) \left (a d - b c\right ) \Gamma{\left (\frac{1}{3},- e \left (c + d x\right )^{3} \right )}}{3 d^{2} \sqrt [3]{- e \left (c + d x\right )^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(e*(d*x+c)**3)*(b*x+a),x)
[Out]
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Mathematica [A] time = 0.583249, size = 0, normalized size = 0. \[ \int e^{e (c+d x)^3} (a+b x) \, dx \]
Verification is Not applicable to the result.
[In] Integrate[E^(e*(c + d*x)^3)*(a + b*x),x]
[Out]
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Maple [F] time = 0.027, size = 0, normalized size = 0. \[ \int{{\rm e}^{e \left ( dx+c \right ) ^{3}}} \left ( bx+a \right ) \, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(e*(d*x+c)^3)*(b*x+a),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (b x + a\right )} e^{\left ({\left (d x + c\right )}^{3} e\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*e^((d*x + c)^3*e),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.255587, size = 144, normalized size = 1.57 \[ -\frac{b d \Gamma \left (\frac{2}{3}, -d^{3} e x^{3} - 3 \, c d^{2} e x^{2} - 3 \, c^{2} d e x - c^{3} e\right ) - \left (-d^{3} e\right )^{\frac{1}{3}}{\left (b c - a d\right )} \Gamma \left (\frac{1}{3}, -d^{3} e x^{3} - 3 \, c d^{2} e x^{2} - 3 \, c^{2} d e x - c^{3} e\right )}{3 \, \left (-d^{3} e\right )^{\frac{2}{3}} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*e^((d*x + c)^3*e),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),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (b x + a\right )} e^{\left ({\left (d x + c\right )}^{3} e\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*e^((d*x + c)^3*e),x, algorithm="giac")
[Out]