Optimal. Leaf size=10 \[ a \sin (x)-b \cos (x) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \[ a \sin (x)-b \cos (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 10, normalized size = 1.00 \[ -b \cos \relax (x) + a \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.83, size = 10, normalized size = 1.00 \[ -b \cos \relax (x) + a \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 11, normalized size = 1.10 \[ -b \cos \relax (x )+a \sin \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 10, normalized size = 1.00 \[ -b \cos \relax (x) + a \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.40, size = 10, normalized size = 1.00 \[ a\,\sin \relax (x)-b\,\cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 8, normalized size = 0.80 \[ a \sin {\relax (x )} - b \cos {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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