Optimal. Leaf size=6 \[ \sin (x) (-\cos (x)) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 6, normalized size of antiderivative = 1.00, 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.
[In]
[Out]
Rule 8
Rule 2635
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 = 0.00, size = 8, normalized size = 1.33 \[ -\frac {1}{2} \sin (2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 6, normalized size = 1.00 \[ -\cos \relax (x) \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.12, size = 6, normalized size = 1.00 \[ -\frac {1}{2} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 7, normalized size = 1.17 \[ -\cos \relax (x ) \sin \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.32, size = 6, normalized size = 1.00 \[ -\frac {1}{2} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.94, size = 6, normalized size = 1.00 \[ -\frac {\sin \left (2\,x\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.06, size = 7, normalized size = 1.17 \[ - \sin {\relax (x )} \cos {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________