Optimal. Leaf size=22 \[ \frac{3 x}{2}+\cos (2 x)-\frac{1}{4} \sin (2 x) \cos (2 x) \]
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Rubi [A] time = 0.0090706, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {2644} \[ \frac{3 x}{2}+\cos (2 x)-\frac{1}{4} \sin (2 x) \cos (2 x) \]
Antiderivative was successfully verified.
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Rule 2644
Rubi steps
\begin{align*} \int (1-\sin (2 x))^2 \, dx &=\frac{3 x}{2}+\cos (2 x)-\frac{1}{4} \cos (2 x) \sin (2 x)\\ \end{align*}
Mathematica [A] time = 0.0077577, size = 18, normalized size = 0.82 \[ \frac{3 x}{2}-\frac{1}{8} \sin (4 x)+\cos (2 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.023, size = 19, normalized size = 0.9 \begin{align*}{\frac{3\,x}{2}}+\cos \left ( 2\,x \right ) -{\frac{\cos \left ( 2\,x \right ) \sin \left ( 2\,x \right ) }{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.935611, size = 19, normalized size = 0.86 \begin{align*} \frac{3}{2} \, x + \cos \left (2 \, x\right ) - \frac{1}{8} \, \sin \left (4 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.97602, size = 58, normalized size = 2.64 \begin{align*} -\frac{1}{4} \, \cos \left (2 \, x\right ) \sin \left (2 \, x\right ) + \frac{3}{2} \, x + \cos \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.17712, size = 37, normalized size = 1.68 \begin{align*} \frac{x \sin ^{2}{\left (2 x \right )}}{2} + \frac{x \cos ^{2}{\left (2 x \right )}}{2} + x - \frac{\sin{\left (2 x \right )} \cos{\left (2 x \right )}}{4} + \cos{\left (2 x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0555, size = 19, normalized size = 0.86 \begin{align*} \frac{3}{2} \, x + \cos \left (2 \, x\right ) - \frac{1}{8} \, \sin \left (4 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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