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 = 0.01, 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 = {2208} \[ -\frac {(c+d x) \text {Gamma}\left (\frac {1}{3},-e (c+d x)^3\right )}{3 d \sqrt [3]{-e (c+d x)^3}} \]
Antiderivative was successfully verified.
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Rule 2208
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 = 0.01, size = 40, normalized size = 1.00 \[ -\frac {(c+d x) \Gamma \left (\frac {1}{3},-e (c+d x)^3\right )}{3 d \sqrt [3]{-e (c+d x)^3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 52, normalized size = 1.30 \[ \frac {\left (-d^{3} e\right )^{\frac {2}{3}} \Gamma \left (\frac {1}{3}, -d^{3} e x^{3} - 3 \, c d^{2} e x^{2} - 3 \, c^{2} d e x - c^{3} e\right )}{3 \, d^{3} e} \]
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 \[ \int e^{\left ({\left (d x + c\right )}^{3} e\right )}\,{d x} \]
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 \[ \int {\mathrm e}^{\left (d x +c \right )^{3} e}\, dx \]
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 \[ \int e^{\left ({\left (d x + c\right )}^{3} e\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.02 \[ \int {\mathrm {e}}^{e\,{\left (c+d\,x\right )}^3} \,d x \]
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 \[ e^{c^{3} e} \int e^{d^{3} e x^{3}} e^{3 c d^{2} e x^{2}} e^{3 c^{2} d e x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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