Optimal. Leaf size=40 \[ -\frac {(c+d x) \Gamma \left (\frac {1}{3},-e (c+d x)^3\right )}{3 d \sqrt [3]{-e (c+d x)^3}} \]
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Rubi [A]
time = 0.00, antiderivative size = 40, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2239}
\begin {gather*} -\frac {(c+d x) \text {Gamma}\left (\frac {1}{3},-e (c+d x)^3\right )}{3 d \sqrt [3]{-e (c+d x)^3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2239
Rubi steps
\begin {align*} \int e^{e (c+d x)^3} \, dx &=-\frac {(c+d x) \Gamma \left (\frac {1}{3},-e (c+d x)^3\right )}{3 d \sqrt [3]{-e (c+d x)^3}}\\ \end {align*}
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Mathematica [A]
time = 0.05, size = 40, normalized size = 1.00 \begin {gather*} -\frac {(c+d x) \Gamma \left (\frac {1}{3},-e (c+d x)^3\right )}{3 d \sqrt [3]{-e (c+d x)^3}} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.00, size = 0, normalized size = 0.00 \[\int {\mathrm e}^{e \left (d x +c \right )^{3}}\, dx\]
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 = 0.13, size = 49, normalized size = 1.22 \begin {gather*} \frac {\left (-d^{3} e\right )^{\frac {2}{3}} e^{\left (-1\right )} \Gamma \left (\frac {1}{3}, -{\left (d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right )} e\right )}{3 \, d^{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^{c^{3} e} \int e^{d^{3} e x^{3}} e^{3 c d^{2} e x^{2}} e^{3 c^{2} d e 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 = -0.02 \begin {gather*} \int {\mathrm {e}}^{e\,{\left (c+d\,x\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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