Optimal. Leaf size=11 \[ \frac{2 \sin (a+b x)}{b} \]
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Rubi [A] time = 0.0165524, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {4288, 2637} \[ \frac{2 \sin (a+b x)}{b} \]
Antiderivative was successfully verified.
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Rule 4288
Rule 2637
Rubi steps
\begin{align*} \int \csc (a+b x) \sin (2 a+2 b x) \, dx &=2 \int \cos (a+b x) \, dx\\ &=\frac{2 \sin (a+b x)}{b}\\ \end{align*}
Mathematica [B] time = 0.0081312, size = 23, normalized size = 2.09 \[ 2 \left (\frac{\sin (a) \cos (b x)}{b}+\frac{\cos (a) \sin (b x)}{b}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.018, size = 12, normalized size = 1.1 \begin{align*} 2\,{\frac{\sin \left ( bx+a \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07669, size = 15, normalized size = 1.36 \begin{align*} \frac{2 \, \sin \left (b x + a\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.46841, size = 24, normalized size = 2.18 \begin{align*} \frac{2 \, \sin \left (b x + a\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.30253, size = 15, normalized size = 1.36 \begin{align*} \frac{2 \, \sin \left (b x + a\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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