Optimal. Leaf size=35 \[ \frac {7}{195} e^{4 x^3} \sin \left (7 x^3\right )+\frac {4}{195} e^{4 x^3} \cos \left (7 x^3\right ) \]
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Rubi [A] time = 0.18, antiderivative size = 35, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {6715, 4433} \[ \frac {7}{195} e^{4 x^3} \sin \left (7 x^3\right )+\frac {4}{195} e^{4 x^3} \cos \left (7 x^3\right ) \]
Antiderivative was successfully verified.
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Rule 4433
Rule 6715
Rubi steps
\begin {align*} \int e^{4 x^3} x^2 \cos \left (7 x^3\right ) \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int e^{4 x} \cos (7 x) \, dx,x,x^3\right )\\ &=\frac {4}{195} e^{4 x^3} \cos \left (7 x^3\right )+\frac {7}{195} e^{4 x^3} \sin \left (7 x^3\right )\\ \end {align*}
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Mathematica [A] time = 0.06, size = 28, normalized size = 0.80 \[ \frac {1}{195} e^{4 x^3} \left (7 \sin \left (7 x^3\right )+4 \cos \left (7 x^3\right )\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 29, normalized size = 0.83 \[ \frac {4}{195} \, \cos \left (7 \, x^{3}\right ) e^{\left (4 \, x^{3}\right )} + \frac {7}{195} \, e^{\left (4 \, x^{3}\right )} \sin \left (7 \, x^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 25, normalized size = 0.71 \[ \frac {1}{195} \, {\left (4 \, \cos \left (7 \, x^{3}\right ) + 7 \, \sin \left (7 \, x^{3}\right )\right )} e^{\left (4 \, x^{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 53, normalized size = 1.51 \[ \frac {-\frac {4 \,{\mathrm e}^{4 x^{3}} \left (\tan ^{2}\left (\frac {7 x^{3}}{2}\right )\right )}{195}+\frac {14 \,{\mathrm e}^{4 x^{3}} \tan \left (\frac {7 x^{3}}{2}\right )}{195}+\frac {4 \,{\mathrm e}^{4 x^{3}}}{195}}{\tan ^{2}\left (\frac {7 x^{3}}{2}\right )+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.86, size = 29, normalized size = 0.83 \[ \frac {4}{195} \, \cos \left (7 \, x^{3}\right ) e^{\left (4 \, x^{3}\right )} + \frac {7}{195} \, e^{\left (4 \, x^{3}\right )} \sin \left (7 \, x^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.59, size = 25, normalized size = 0.71 \[ \frac {{\mathrm {e}}^{4\,x^3}\,\left (4\,\cos \left (7\,x^3\right )+7\,\sin \left (7\,x^3\right )\right )}{195} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.82, size = 32, normalized size = 0.91 \[ \frac {7 e^{4 x^{3}} \sin {\left (7 x^{3} \right )}}{195} + \frac {4 e^{4 x^{3}} \cos {\left (7 x^{3} \right )}}{195} \]
Verification of antiderivative is not currently implemented for this CAS.
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