Optimal. Leaf size=10 \[ a \sin (x)-b \cos (x) \]
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Rubi [A] time = 0.00609, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {2637, 2638} \[ a \sin (x)-b \cos (x) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 2638
Rubi steps
\begin{align*} \int (a \cos (x)+b \sin (x)) \, dx &=a \int \cos (x) \, dx+b \int \sin (x) \, dx\\ &=-b \cos (x)+a \sin (x)\\ \end{align*}
Mathematica [A] time = 0.0018502, size = 10, normalized size = 1. \[ a \sin (x)-b \cos (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 11, normalized size = 1.1 \begin{align*} -b\cos \left ( x \right ) +a\sin \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00208, size = 14, normalized size = 1.4 \begin{align*} -b \cos \left (x\right ) + a \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.46018, size = 30, normalized size = 3. \begin{align*} -b \cos \left (x\right ) + a \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.059447, size = 8, normalized size = 0.8 \begin{align*} a \sin{\left (x \right )} - b \cos{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13656, size = 14, normalized size = 1.4 \begin{align*} -b \cos \left (x\right ) + a \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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