Optimal. Leaf size=25 \[ -\frac {1}{8} \cos (2 x)-\frac {1}{16} \cos (4 x)+\frac {1}{24} \cos (6 x) \]
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Rubi [A] time = 0.03, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {4355, 2638} \[ -\frac {1}{8} \cos (2 x)-\frac {1}{16} \cos (4 x)+\frac {1}{24} \cos (6 x) \]
Antiderivative was successfully verified.
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Rule 2638
Rule 4355
Rubi steps
\begin {align*} \int \sin (x) \sin (2 x) \sin (3 x) \, dx &=\int \left (\frac {1}{4} \sin (2 x)+\frac {1}{4} \sin (4 x)-\frac {1}{4} \sin (6 x)\right ) \, dx\\ &=\frac {1}{4} \int \sin (2 x) \, dx+\frac {1}{4} \int \sin (4 x) \, dx-\frac {1}{4} \int \sin (6 x) \, dx\\ &=-\frac {1}{8} \cos (2 x)-\frac {1}{16} \cos (4 x)+\frac {1}{24} \cos (6 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 1.00 \[ -\frac {1}{8} \cos (2 x)-\frac {1}{16} \cos (4 x)+\frac {1}{24} \cos (6 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 17, normalized size = 0.68 \[ \frac {4}{3} \, \cos \relax (x)^{6} - \frac {5}{2} \, \cos \relax (x)^{4} + \cos \relax (x)^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 13, normalized size = 0.52 \[ -\frac {4}{3} \, \sin \relax (x)^{6} + \frac {3}{2} \, \sin \relax (x)^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 20, normalized size = 0.80 \[ -\frac {\cos \left (2 x \right )}{8}-\frac {\cos \left (4 x \right )}{16}+\frac {\cos \left (6 x \right )}{24} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 19, normalized size = 0.76 \[ \frac {1}{24} \, \cos \left (6 \, x\right ) - \frac {1}{16} \, \cos \left (4 \, x\right ) - \frac {1}{8} \, \cos \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.22, size = 14, normalized size = 0.56 \[ -\frac {{\sin \relax (x)}^4\,\left (8\,{\sin \relax (x)}^2-9\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 13.25, size = 114, normalized size = 4.56 \[ \frac {x \sin {\relax (x )} \sin {\left (2 x \right )} \sin {\left (3 x \right )}}{4} + \frac {x \sin {\relax (x )} \cos {\left (2 x \right )} \cos {\left (3 x \right )}}{4} + \frac {x \sin {\left (2 x \right )} \cos {\relax (x )} \cos {\left (3 x \right )}}{4} - \frac {x \sin {\left (3 x \right )} \cos {\relax (x )} \cos {\left (2 x \right )}}{4} - \frac {5 \sin {\relax (x )} \sin {\left (2 x \right )} \cos {\left (3 x \right )}}{24} - \frac {\sin {\left (2 x \right )} \sin {\left (3 x \right )} \cos {\relax (x )}}{8} - \frac {\cos {\relax (x )} \cos {\left (2 x \right )} \cos {\left (3 x \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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