Optimal. Leaf size=12 \[ \frac{\cos (2 \pi x)}{2 \pi } \]
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Rubi [A] time = 0.0045919, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {2638} \[ \frac{\cos (2 \pi x)}{2 \pi } \]
Antiderivative was successfully verified.
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Rule 2638
Rubi steps
\begin{align*} \int \sin (\pi (1+2 x)) \, dx &=\frac{\cos (2 \pi x)}{2 \pi }\\ \end{align*}
Mathematica [A] time = 0.0050726, size = 12, normalized size = 1. \[ \frac{\cos (2 \pi x)}{2 \pi } \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 11, normalized size = 0.9 \begin{align*}{\frac{\cos \left ( 2\,\pi \,x \right ) }{2\,\pi }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.951001, size = 14, normalized size = 1.17 \begin{align*} \frac{\cos \left (2 \, \pi x\right )}{2 \, \pi } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.92326, size = 35, normalized size = 2.92 \begin{align*} -\frac{\cos \left (\pi + 2 \, \pi x\right )}{2 \, \pi } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.04472, size = 12, normalized size = 1. \begin{align*} - \frac{\cos{\left (\pi \left (2 x + 1\right ) \right )}}{2 \pi } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08439, size = 14, normalized size = 1.17 \begin{align*} \frac{\cos \left (2 \, \pi x\right )}{2 \, \pi } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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