Optimal. Leaf size=25 \[ \frac {1}{4} \sin (2 x)-\frac {1}{40} \sin (10 x)-\frac {1}{56} \sin (14 x) \]
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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 = {4354, 2637} \[ \frac {1}{4} \sin (2 x)-\frac {1}{40} \sin (10 x)-\frac {1}{56} \sin (14 x) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 4354
Rubi steps
\begin {align*} \int \cos (2 x) \sin ^2(6 x) \, dx &=\int \left (\frac {1}{2} \cos (2 x)-\frac {1}{4} \cos (10 x)-\frac {1}{4} \cos (14 x)\right ) \, dx\\ &=-\left (\frac {1}{4} \int \cos (10 x) \, dx\right )-\frac {1}{4} \int \cos (14 x) \, dx+\frac {1}{2} \int \cos (2 x) \, dx\\ &=\frac {1}{4} \sin (2 x)-\frac {1}{40} \sin (10 x)-\frac {1}{56} \sin (14 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 25, normalized size = 1.00 \[ \frac {1}{4} \sin (2 x)-\frac {1}{40} \sin (10 x)-\frac {1}{56} \sin (14 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 2.01, size = 32, normalized size = 1.28 \[ -\frac {1}{70} \, {\left (80 \, \cos \left (2 \, x\right )^{6} - 72 \, \cos \left (2 \, x\right )^{4} + 9 \, \cos \left (2 \, x\right )^{2} - 17\right )} \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 19, normalized size = 0.76 \[ -\frac {1}{56} \, \sin \left (14 \, x\right ) - \frac {1}{40} \, \sin \left (10 \, x\right ) + \frac {1}{4} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 20, normalized size = 0.80 \[ \frac {\sin \left (2 x \right )}{4}-\frac {\sin \left (10 x \right )}{40}-\frac {\sin \left (14 x \right )}{56} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 19, normalized size = 0.76 \[ -\frac {1}{56} \, \sin \left (14 \, x\right ) - \frac {1}{40} \, \sin \left (10 \, x\right ) + \frac {1}{4} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.29, size = 25, normalized size = 1.00 \[ \frac {8\,{\sin \left (2\,x\right )}^7}{7}-\frac {12\,{\sin \left (2\,x\right )}^5}{5}+\frac {3\,{\sin \left (2\,x\right )}^3}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.73, size = 48, normalized size = 1.92 \[ \frac {17 \sin {\left (2 x \right )} \sin ^{2}{\left (6 x \right )}}{70} + \frac {9 \sin {\left (2 x \right )} \cos ^{2}{\left (6 x \right )}}{35} - \frac {3 \sin {\left (6 x \right )} \cos {\left (2 x \right )} \cos {\left (6 x \right )}}{35} \]
Verification of antiderivative is not currently implemented for this CAS.
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