Optimal. Leaf size=15 \[ \frac {\sin (x)}{2}+\frac {1}{14} \sin (7 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {4368}
\begin {gather*} \frac {\sin (x)}{2}+\frac {1}{14} \sin (7 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 4368
Rubi steps
\begin {align*} \int \cos (3 x) \cos (4 x) \, dx &=\frac {\sin (x)}{2}+\frac {1}{14} \sin (7 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} \frac {\sin (x)}{2}+\frac {1}{14} \sin (7 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 12, normalized size = 0.80
method | result | size |
default | \(\frac {\sin \left (x \right )}{2}+\frac {\sin \left (7 x \right )}{14}\) | \(12\) |
risch | \(\frac {\sin \left (x \right )}{2}+\frac {\sin \left (7 x \right )}{14}\) | \(12\) |
norman | \(\frac {-\frac {8 \tan \left (2 x \right ) \left (\tan ^{2}\left (\frac {3 x}{2}\right )\right )}{7}+\frac {6 \left (\tan ^{2}\left (2 x \right )\right ) \tan \left (\frac {3 x}{2}\right )}{7}+\frac {8 \tan \left (2 x \right )}{7}-\frac {6 \tan \left (\frac {3 x}{2}\right )}{7}}{\left (1+\tan ^{2}\left (\frac {3 x}{2}\right )\right ) \left (1+\tan ^{2}\left (2 x \right )\right )}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 6.02, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{14} \, \sin \left (7 \, x\right ) + \frac {1}{2} \, \sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 24 vs.
\(2 (11) = 22\).
time = 0.58, size = 24, normalized size = 1.60 \begin {gather*} \frac {1}{7} \, {\left (32 \, \cos \left (x\right )^{6} - 40 \, \cos \left (x\right )^{4} + 12 \, \cos \left (x\right )^{2} + 3\right )} \sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 26 vs.
\(2 (10) = 20\).
time = 0.12, size = 26, normalized size = 1.73 \begin {gather*} - \frac {3 \sin {\left (3 x \right )} \cos {\left (4 x \right )}}{7} + \frac {4 \sin {\left (4 x \right )} \cos {\left (3 x \right )}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.14, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{14} \, \sin \left (7 \, x\right ) + \frac {1}{2} \, \sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 11, normalized size = 0.73 \begin {gather*} \frac {\sin \left (7\,x\right )}{14}+\frac {\sin \left (x\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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