Optimal. Leaf size=15 \[ 5 e^{-6-4 x^3}+x^3 \]
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Rubi [A] time = 0.08, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 4, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {6688, 12, 14, 2209} \begin {gather*} x^3+5 e^{-4 x^3-6} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2209
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int 3 \left (1-20 e^{-6-4 x^3}\right ) x^2 \, dx\\ &=3 \int \left (1-20 e^{-6-4 x^3}\right ) x^2 \, dx\\ &=3 \int \left (x^2-20 e^{-6-4 x^3} x^2\right ) \, dx\\ &=x^3-60 \int e^{-6-4 x^3} x^2 \, dx\\ &=5 e^{-6-4 x^3}+x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 15, normalized size = 1.00 \begin {gather*} 5 e^{-6-4 x^3}+x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 23, normalized size = 1.53 \begin {gather*} {\left (x^{3} e^{\left (4 \, x^{3} + 6\right )} + 5\right )} e^{\left (-4 \, x^{3} - 6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.13, size = 30, normalized size = 2.00 \begin {gather*} \frac {1}{4} \, {\left (4 \, x^{3} e^{6} - {\left (e^{\left (4 \, x^{3} + 6\right )} - 20\right )} e^{\left (-4 \, x^{3}\right )}\right )} e^{\left (-6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 15, normalized size = 1.00
method | result | size |
risch | \(x^{3}+5 \,{\mathrm e}^{-4 x^{3}-6}\) | \(15\) |
default | \(x^{3}+5 \,{\mathrm e}^{-4 x^{3}} {\mathrm e}^{-6}\) | \(17\) |
norman | \(\left (5+x^{3} {\mathrm e}^{4 x^{3}+6}\right ) {\mathrm e}^{-4 x^{3}-6}\) | \(26\) |
meijerg | \(-\frac {{\mathrm e}^{-4 x^{3}+4 x^{3} {\mathrm e}^{-6}} \left (1-{\mathrm e}^{4 x^{3} \left (1-{\mathrm e}^{-6}\right )}\right )}{4 \left (1-{\mathrm e}^{-6}\right )}-5 \,{\mathrm e}^{-4 x^{3}+4 x^{3} {\mathrm e}^{-6}} \left (1-{\mathrm e}^{-4 x^{3} {\mathrm e}^{-6}}\right )\) | \(70\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 14, normalized size = 0.93 \begin {gather*} x^{3} + 5 \, e^{\left (-4 \, x^{3} - 6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.77, size = 14, normalized size = 0.93 \begin {gather*} 5\,{\mathrm {e}}^{-6}\,{\mathrm {e}}^{-4\,x^3}+x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.93 \begin {gather*} x^{3} + 5 e^{- 4 x^{3} - 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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