Optimal. Leaf size=29 \[ \frac {1}{2} (x+2) \sin (\log (3 (x+2)))+\frac {1}{2} (x+2) \cos (\log (3 (x+2))) \]
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Rubi [A] time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {4476} \[ \frac {1}{2} (x+2) \sin (\log (3 (x+2)))+\frac {1}{2} (x+2) \cos (\log (3 (x+2))) \]
Antiderivative was successfully verified.
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Rule 4476
Rubi steps
\begin {align*} \int \cos (\log (6+3 x)) \, dx &=\frac {1}{3} \operatorname {Subst}(\int \cos (\log (x)) \, dx,x,6+3 x)\\ &=\frac {1}{2} (2+x) \cos (\log (3 (2+x)))+\frac {1}{2} (2+x) \sin (\log (3 (2+x)))\\ \end {align*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 0.76 \[ \frac {1}{2} (x+2) (\sin (\log (3 (x+2)))+\cos (\log (3 (x+2)))) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 25, normalized size = 0.86 \[ \frac {1}{2} \, {\left (x + 2\right )} \cos \left (\log \left (3 \, x + 6\right )\right ) + \frac {1}{2} \, {\left (x + 2\right )} \sin \left (\log \left (3 \, x + 6\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 25, normalized size = 0.86 \[ \frac {1}{2} \, {\left (x + 2\right )} \cos \left (\log \left (3 \, x + 6\right )\right ) + \frac {1}{2} \, {\left (x + 2\right )} \sin \left (\log \left (3 \, x + 6\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.05, size = 34, normalized size = 1.17 \[ \left (\frac {1}{4}-\frac {i}{4}\right ) \left (2+x \right ) \left (6+3 x \right )^{i}+\left (\frac {1}{4}+\frac {i}{4}\right ) \left (2+x \right ) \left (6+3 x \right )^{-i} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 20, normalized size = 0.69 \[ \frac {1}{2} \, {\left (x + 2\right )} {\left (\cos \left (\log \left (3 \, x + 6\right )\right ) + \sin \left (\log \left (3 \, x + 6\right )\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.17, size = 21, normalized size = 0.72 \[ \frac {\sqrt {2}\,\sin \left (\frac {\pi }{4}+\ln \left (3\,x+6\right )\right )\,\left (3\,x+6\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \cos {\left (\log {\left (3 x + 6 \right )} \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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