Optimal. Leaf size=32 \[ \frac {e^{x^3}}{3}-\frac {2 e^{5 x^3}}{15}+\frac {e^{9 x^3}}{27} \]
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Rubi [A] time = 0.21, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {6715, 2249, 194} \[ \frac {e^{x^3}}{3}-\frac {2 e^{5 x^3}}{15}+\frac {e^{9 x^3}}{27} \]
Antiderivative was successfully verified.
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Rule 194
Rule 2249
Rule 6715
Rubi steps
\begin {align*} \int e^{x^3} \left (1-e^{4 x^3}\right )^2 x^2 \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int e^x \left (1-e^{4 x}\right )^2 \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (1-x^4\right )^2 \, dx,x,e^{x^3}\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (1-2 x^4+x^8\right ) \, dx,x,e^{x^3}\right )\\ &=\frac {e^{x^3}}{3}-\frac {2 e^{5 x^3}}{15}+\frac {e^{9 x^3}}{27}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 29, normalized size = 0.91 \[ \frac {1}{135} e^{x^3} \left (-18 e^{4 x^3}+5 e^{8 x^3}+45\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 23, normalized size = 0.72 \[ \frac {1}{27} \, e^{\left (9 \, x^{3}\right )} - \frac {2}{15} \, e^{\left (5 \, x^{3}\right )} + \frac {1}{3} \, e^{\left (x^{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 23, normalized size = 0.72 \[ \frac {1}{27} \, e^{\left (9 \, x^{3}\right )} - \frac {2}{15} \, e^{\left (5 \, x^{3}\right )} + \frac {1}{3} \, e^{\left (x^{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 24, normalized size = 0.75 \[ \frac {{\mathrm e}^{x^{3}}}{3}-\frac {2 \,{\mathrm e}^{5 x^{3}}}{15}+\frac {{\mathrm e}^{9 x^{3}}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.81, size = 23, normalized size = 0.72 \[ \frac {1}{27} \, e^{\left (9 \, x^{3}\right )} - \frac {2}{15} \, e^{\left (5 \, x^{3}\right )} + \frac {1}{3} \, e^{\left (x^{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.61, size = 24, normalized size = 0.75 \[ \frac {{\mathrm {e}}^{x^3}\,\left (5\,{\mathrm {e}}^{8\,x^3}-18\,{\mathrm {e}}^{4\,x^3}+45\right )}{135} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 24, normalized size = 0.75 \[ \frac {e^{9 x^{3}}}{27} - \frac {2 e^{5 x^{3}}}{15} + \frac {e^{x^{3}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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