Optimal. Leaf size=29 \[ \frac {1}{2} (2+x) \cos (\log (3 (2+x)))+\frac {1}{2} (2+x) \sin (\log (3 (2+x))) \]
[Out]
________________________________________________________________________________________
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 = {4564}
\begin {gather*} \frac {1}{2} (x+2) \sin (\log (3 (x+2)))+\frac {1}{2} (x+2) \cos (\log (3 (x+2))) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 4564
Rubi steps
\begin {align*} \int \cos (\log (6+3 x)) \, dx &=\frac {1}{3} \text {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*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 22, normalized size = 0.76 \begin {gather*} \frac {1}{2} (2+x) (\cos (\log (3 (2+x)))+\sin (\log (3 (2+x)))) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [C] Result contains complex when optimal does not.
time = 0.04, size = 34, normalized size = 1.17
method | result | size |
risch | \(\left (\frac {1}{4}-\frac {i}{4}\right ) \left (2+x \right ) \left (6+3 x \right )^{i}+\left (\frac {1}{4}+\frac {i}{4}\right ) \left (2+x \right ) \left (6+3 x \right )^{-i}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 20, normalized size = 0.69 \begin {gather*} \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 )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.96, size = 25, normalized size = 0.86 \begin {gather*} \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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \cos {\left (\log {\left (3 x + 6 \right )} \right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 25, normalized size = 0.86 \begin {gather*} \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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 2.17, size = 21, normalized size = 0.72 \begin {gather*} \frac {\sqrt {2}\,\sin \left (\frac {\pi }{4}+\ln \left (3\,x+6\right )\right )\,\left (3\,x+6\right )}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________