Optimal. Leaf size=11 \[ -\frac {\cos (a+b x)}{b} \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 2.00 \[ \frac {\sin (a) \sin (b x)}{b}-\frac {\cos (a) \cos (b x)}{b} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 11, normalized size = 1.00 \[ -\frac {\cos \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 11, normalized size = 1.00 \[ -\frac {\cos \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 1.09 \[ -\frac {\cos \left (b x +a \right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 11, normalized size = 1.00 \[ -\frac {\cos \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 11, normalized size = 1.00 \[ -\frac {\cos \left (a+b\,x\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 14, normalized size = 1.27 \[ \begin {cases} - \frac {\cos {\left (a + b x \right )}}{b} & \text {for}\: b \neq 0 \\x \sin {\relax (a )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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