Optimal. Leaf size=4 \[ -\cos (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2718}
\begin {gather*} -\cos (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2718
Rubi steps
\begin {align*} \int \sin (x) \, dx &=-\cos (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 4, normalized size = 1.00 \begin {gather*} -\cos (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 5, normalized size = 1.25
method | result | size |
lookup | \(-\cos \left (x \right )\) | \(5\) |
default | \(-\cos \left (x \right )\) | \(5\) |
risch | \(-\cos \left (x \right )\) | \(5\) |
norman | \(-\frac {2}{1+\tan ^{2}\left (\frac {x}{2}\right )}\) | \(13\) |
meijerg | \(\sqrt {\pi }\, \left (\frac {1}{\sqrt {\pi }}-\frac {\cos \left (x \right )}{\sqrt {\pi }}\right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.91, size = 4, normalized size = 1.00 \begin {gather*} -\cos \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.62, size = 4, normalized size = 1.00 \begin {gather*} -\cos \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 3, normalized size = 0.75 \begin {gather*} - \cos {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.92, size = 4, normalized size = 1.00 \begin {gather*} -\cos \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 4, normalized size = 1.00 \begin {gather*} -\cos \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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