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 = {2259, 2239}
\begin {gather*} -\frac {(a+b x) \text {Gamma}\left (\frac {1}{3},-(a+b x)^3\right )}{3 b \sqrt [3]{-(a+b x)^3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2239
Rule 2259
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 = 0.04, size = 38, normalized size = 1.00 \begin {gather*} -\frac {(a+b x) \Gamma \left (\frac {1}{3},-(a+b x)^3\right )}{3 b \sqrt [3]{-(a+b x)^3}} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.01, 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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.11, size = 44, normalized size = 1.16 \begin {gather*} \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}} \end {gather*}
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 \begin {gather*} e^{a^{3}} \int e^{b^{3} x^{3}} e^{3 a b^{2} x^{2}} e^{3 a^{2} b x}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int {\mathrm {e}}^{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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