Optimal. Leaf size=31 \[ \frac {\sin (x)}{4}+\frac {1}{12} \sin (3 x)+\frac {1}{28} \sin (7 x)+\frac {1}{36} \sin (9 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps
used = 6, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {4440, 2717}
\begin {gather*} \frac {\sin (x)}{4}+\frac {1}{12} \sin (3 x)+\frac {1}{28} \sin (7 x)+\frac {1}{36} \sin (9 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2717
Rule 4440
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\int \left (\frac {\cos (x)}{4}+\frac {1}{4} \cos (3 x)+\frac {1}{4} \cos (7 x)+\frac {1}{4} \cos (9 x)\right ) \, dx\\ &=\frac {1}{4} \int \cos (x) \, dx+\frac {1}{4} \int \cos (3 x) \, dx+\frac {1}{4} \int \cos (7 x) \, dx+\frac {1}{4} \int \cos (9 x) \, dx\\ &=\frac {\sin (x)}{4}+\frac {1}{12} \sin (3 x)+\frac {1}{28} \sin (7 x)+\frac {1}{36} \sin (9 x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 31, normalized size = 1.00 \begin {gather*} \frac {\sin (x)}{4}+\frac {1}{12} \sin (3 x)+\frac {1}{28} \sin (7 x)+\frac {1}{36} \sin (9 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.62, size = 24, normalized size = 0.77
method | result | size |
default | \(\frac {\sin \left (x \right )}{4}+\frac {\sin \left (3 x \right )}{12}+\frac {\sin \left (7 x \right )}{28}+\frac {\sin \left (9 x \right )}{36}\) | \(24\) |
risch | \(\frac {\sin \left (x \right )}{4}+\frac {\sin \left (3 x \right )}{12}+\frac {\sin \left (7 x \right )}{28}+\frac {\sin \left (9 x \right )}{36}\) | \(24\) |
parallelrisch | \(\frac {\sin \left (x \right )}{4}+\frac {\sin \left (3 x \right )}{12}+\frac {\sin \left (7 x \right )}{28}+\frac {\sin \left (9 x \right )}{36}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.39, size = 23, normalized size = 0.74 \begin {gather*} \frac {1}{36} \, \sin \left (9 \, x\right ) + \frac {1}{28} \, \sin \left (7 \, x\right ) + \frac {1}{12} \, \sin \left (3 \, x\right ) + \frac {1}{4} \, \sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.62, size = 30, normalized size = 0.97 \begin {gather*} \frac {1}{63} \, {\left (448 \, \cos \left (x\right )^{8} - 640 \, \cos \left (x\right )^{6} + 240 \, \cos \left (x\right )^{4} + 5 \, \cos \left (x\right )^{2} + 10\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. 66 vs.
\(2 (24) = 48\).
time = 1.34, size = 66, normalized size = 2.13 \begin {gather*} - \frac {10 \sin {\left (x \right )} \sin {\left (3 x \right )} \sin {\left (5 x \right )}}{63} - \frac {11 \sin {\left (x \right )} \cos {\left (3 x \right )} \cos {\left (5 x \right )}}{63} - \frac {17 \sin {\left (3 x \right )} \cos {\left (x \right )} \cos {\left (5 x \right )}}{63} + \frac {25 \sin {\left (5 x \right )} \cos {\left (x \right )} \cos {\left (3 x \right )}}{63} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.48, size = 23, normalized size = 0.74 \begin {gather*} \frac {1}{36} \, \sin \left (9 \, x\right ) + \frac {1}{28} \, \sin \left (7 \, x\right ) + \frac {1}{12} \, \sin \left (3 \, x\right ) + \frac {1}{4} \, \sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.28, size = 27, normalized size = 0.87 \begin {gather*} \frac {64\,{\sin \left (x\right )}^9}{9}-\frac {128\,{\sin \left (x\right )}^7}{7}+16\,{\sin \left (x\right )}^5-\frac {17\,{\sin \left (x\right )}^3}{3}+\sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 19, normalized size = 0.61 \begin {gather*} \frac {\sin \left (8 x \right )}{48}+\frac {\sin \left (6 x \right )}{12}+\frac {\sin \left (2 x \right )}{24} \end {gather*}
Warning: Unable to verify antiderivative.
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