Optimal. Leaf size=31 \[ \frac{1}{9} \cos ^3\left (\frac{\pi }{12}-3 x\right )-\frac{1}{3} \cos \left (\frac{\pi }{12}-3 x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0107794, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {2633} \[ \frac{1}{9} \cos ^3\left (\frac{\pi }{12}-3 x\right )-\frac{1}{3} \cos \left (\frac{\pi }{12}-3 x\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2633
Rubi steps
\begin{align*} \int -\sin ^3\left (\frac{\pi }{12}-3 x\right ) \, dx &=-\left (\frac{1}{3} \operatorname{Subst}\left (\int \left (1-x^2\right ) \, dx,x,\cos \left (\frac{\pi }{12}-3 x\right )\right )\right )\\ &=-\frac{1}{3} \cos \left (\frac{\pi }{12}-3 x\right )+\frac{1}{9} \cos ^3\left (\frac{\pi }{12}-3 x\right )\\ \end{align*}
Mathematica [A] time = 0.0163376, size = 31, normalized size = 1. \[ \frac{1}{36} \cos \left (3 \left (\frac{\pi }{12}-3 x\right )\right )-\frac{1}{4} \cos \left (\frac{\pi }{12}-3 x\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 23, normalized size = 0.7 \begin{align*} -{\frac{1}{9} \left ( 2+ \left ( \cos \left ({\frac{5\,\pi }{12}}+3\,x \right ) \right ) ^{2} \right ) \sin \left ({\frac{5\,\pi }{12}}+3\,x \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.936318, size = 31, normalized size = 1. \begin{align*} \frac{1}{9} \, \sin \left (\frac{5}{12} \, \pi + 3 \, x\right )^{3} - \frac{1}{3} \, \sin \left (\frac{5}{12} \, \pi + 3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.5673, size = 70, normalized size = 2.26 \begin{align*} -\frac{1}{9} \,{\left (\cos \left (\frac{5}{12} \, \pi + 3 \, x\right )^{2} + 2\right )} \sin \left (\frac{5}{12} \, \pi + 3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.309147, size = 39, normalized size = 1.26 \begin{align*} - \frac{2 \sin ^{3}{\left (3 x + \frac{5 \pi }{12} \right )}}{9} - \frac{\sin{\left (3 x + \frac{5 \pi }{12} \right )} \cos ^{2}{\left (3 x + \frac{5 \pi }{12} \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.06113, size = 31, normalized size = 1. \begin{align*} \frac{1}{9} \, \sin \left (\frac{5}{12} \, \pi + 3 \, x\right )^{3} - \frac{1}{3} \, \sin \left (\frac{5}{12} \, \pi + 3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]