Optimal. Leaf size=38 \[ -\frac {(a+b x) \Gamma \left (\frac {1}{3},-(a+b x)^3\right )}{3 b \sqrt [3]{-(a+b x)^3}} \]
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Rubi [A] time = 0.01, antiderivative size = 38, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {2227, 2208} \[ -\frac {(a+b x) \text {Gamma}\left (\frac {1}{3},-(a+b x)^3\right )}{3 b \sqrt [3]{-(a+b x)^3}} \]
Antiderivative was successfully verified.
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Rule 2208
Rule 2227
Rubi steps
\begin {align*} \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} \, dx &=\int e^{(a+b x)^3} \, dx\\ &=-\frac {(a+b x) \Gamma \left (\frac {1}{3},-(a+b x)^3\right )}{3 b \sqrt [3]{-(a+b x)^3}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 38, normalized size = 1.00 \[ -\frac {(a+b x) \Gamma \left (\frac {1}{3},-(a+b x)^3\right )}{3 b \sqrt [3]{-(a+b x)^3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 44, normalized size = 1.16 \[ \frac {\left (-b^{3}\right )^{\frac {2}{3}} \Gamma \left (\frac {1}{3}, -b^{3} x^{3} - 3 \, a b^{2} x^{2} - 3 \, a^{2} b x - a^{3}\right )}{3 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.03, size = 0, normalized size = 0.00 \[ \int {\mathrm e}^{b^{3} x^{3}+3 a \,b^{2} x^{2}+3 a^{2} b x +a^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int e^{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \[ \int {\mathrm {e}}^{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ e^{a^{3}} \int e^{b^{3} x^{3}} e^{3 a b^{2} x^{2}} e^{3 a^{2} b x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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