Optimal. Leaf size=11 \[ -\frac{\cos (a+b x)}{b} \]
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Rubi [A] time = 0.0035687, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {2638} \[ -\frac{\cos (a+b x)}{b} \]
Antiderivative was successfully verified.
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Rule 2638
Rubi steps
\begin{align*} \int \sin (a+b x) \, dx &=-\frac{\cos (a+b x)}{b}\\ \end{align*}
Mathematica [A] time = 0.0092239, size = 22, normalized size = 2. \[ \frac{\sin (a) \sin (b x)}{b}-\frac{\cos (a) \cos (b x)}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 12, normalized size = 1.1 \begin{align*} -{\frac{\cos \left ( bx+a \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.940373, size = 15, normalized size = 1.36 \begin{align*} -\frac{\cos \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 = 1.75709, size = 23, normalized size = 2.09 \begin{align*} -\frac{\cos \left (b x + a\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.125937, size = 14, normalized size = 1.27 \begin{align*} \begin{cases} - \frac{\cos{\left (a + b x \right )}}{b} & \text{for}\: b \neq 0 \\x \sin{\left (a \right )} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07024, size = 15, normalized size = 1.36 \begin{align*} -\frac{\cos \left (b x + a\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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