Optimal. Leaf size=19 \[ \frac {\sin \left (x^3\right )}{6}+\frac {1}{54} \sin \left (9 x^3\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 3, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {4572, 3380, 2637} \[ \frac {\sin \left (x^3\right )}{6}+\frac {1}{54} \sin \left (9 x^3\right ) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 3380
Rule 4572
Rubi steps
\begin {align*} \int x^2 \cos \left (4 x^3\right ) \cos \left (5 x^3\right ) \, dx &=\int \left (\frac {1}{2} x^2 \cos \left (x^3\right )+\frac {1}{2} x^2 \cos \left (9 x^3\right )\right ) \, dx\\ &=\frac {1}{2} \int x^2 \cos \left (x^3\right ) \, dx+\frac {1}{2} \int x^2 \cos \left (9 x^3\right ) \, dx\\ &=\frac {1}{6} \operatorname {Subst}\left (\int \cos (x) \, dx,x,x^3\right )+\frac {1}{6} \operatorname {Subst}\left (\int \cos (9 x) \, dx,x,x^3\right )\\ &=\frac {\sin \left (x^3\right )}{6}+\frac {1}{54} \sin \left (9 x^3\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.00 \[ \frac {\sin \left (x^3\right )}{6}+\frac {1}{54} \sin \left (9 x^3\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.50, size = 40, normalized size = 2.11 \[ \frac {1}{27} \, {\left (128 \, \cos \left (x^{3}\right )^{8} - 224 \, \cos \left (x^{3}\right )^{6} + 120 \, \cos \left (x^{3}\right )^{4} - 20 \, \cos \left (x^{3}\right )^{2} + 5\right )} \sin \left (x^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.14, size = 39, normalized size = 2.05 \[ \frac {128}{27} \, \sin \left (x^{3}\right )^{9} - \frac {32}{3} \, \sin \left (x^{3}\right )^{7} + 8 \, \sin \left (x^{3}\right )^{5} - \frac {20}{9} \, \sin \left (x^{3}\right )^{3} + \frac {1}{3} \, \sin \left (x^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.23, size = 16, normalized size = 0.84 \[ \frac {\sin \left (x^{3}\right )}{6}+\frac {\sin \left (9 x^{3}\right )}{54} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 15, normalized size = 0.79 \[ \frac {1}{54} \, \sin \left (9 \, x^{3}\right ) + \frac {1}{6} \, \sin \left (x^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.03, size = 15, normalized size = 0.79 \[ \frac {\sin \left (x^3\right )}{6}+\frac {\sin \left (9\,x^3\right )}{54} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 5.25, size = 32, normalized size = 1.68 \[ - \frac {4 \sin {\left (4 x^{3} \right )} \cos {\left (5 x^{3} \right )}}{27} + \frac {5 \sin {\left (5 x^{3} \right )} \cos {\left (4 x^{3} \right )}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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