Optimal. Leaf size=6 \[ \sin (x) (-\cos (x)) \]
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Rubi [A] time = 0.0110818, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {2635, 8} \[ \sin (x) (-\cos (x)) \]
Antiderivative was successfully verified.
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Rule 2635
Rule 8
Rubi steps
\begin{align*} \int \left (-\cos ^2(x)+\sin ^2(x)\right ) \, dx &=-\int \cos ^2(x) \, dx+\int \sin ^2(x) \, dx\\ &=-\cos (x) \sin (x)\\ \end{align*}
Mathematica [A] time = 0.0023956, size = 8, normalized size = 1.33 \[ -\frac{1}{2} \sin (2 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 7, normalized size = 1.2 \begin{align*} -\cos \left ( x \right ) \sin \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.952364, size = 8, normalized size = 1.33 \begin{align*} -\frac{1}{2} \, \sin \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.09111, size = 22, normalized size = 3.67 \begin{align*} -\cos \left (x\right ) \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058978, size = 7, normalized size = 1.17 \begin{align*} - \sin{\left (x \right )} \cos{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05358, size = 8, normalized size = 1.33 \begin{align*} -\frac{1}{2} \, \sin \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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