Optimal. Leaf size=17 \[ \frac{\sin ^4(x)}{4}-\frac{\sin ^6(x)}{6} \]
[Out]
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Rubi [A] time = 0.0351594, antiderivative size = 17, 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 \[ \frac{\sin ^4(x)}{4}-\frac{\sin ^6(x)}{6} \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^3*Sin[x]^3,x]
[Out]
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Rubi in Sympy [A] time = 2.42613, size = 12, normalized size = 0.71 \[ - \frac{\sin ^{6}{\left (x \right )}}{6} + \frac{\sin ^{4}{\left (x \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**3*sin(x)**3,x)
[Out]
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Mathematica [A] time = 0.00985004, size = 17, normalized size = 1. \[ \frac{1}{192} \cos (6 x)-\frac{3}{64} \cos (2 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^3*Sin[x]^3,x]
[Out]
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Maple [A] time = 0.01, size = 18, normalized size = 1.1 \[ -{\frac{ \left ( \cos \left ( x \right ) \right ) ^{4} \left ( \sin \left ( x \right ) \right ) ^{2}}{6}}-{\frac{ \left ( \cos \left ( x \right ) \right ) ^{4}}{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^3*sin(x)^3,x)
[Out]
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Maxima [A] time = 1.3473, size = 18, normalized size = 1.06 \[ -\frac{1}{6} \, \sin \left (x\right )^{6} + \frac{1}{4} \, \sin \left (x\right )^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^3*sin(x)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217586, size = 18, normalized size = 1.06 \[ \frac{1}{6} \, \cos \left (x\right )^{6} - \frac{1}{4} \, \cos \left (x\right )^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^3*sin(x)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.044095, size = 12, normalized size = 0.71 \[ - \frac{\sin ^{6}{\left (x \right )}}{6} + \frac{\sin ^{4}{\left (x \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**3*sin(x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.20138, size = 18, normalized size = 1.06 \[ \frac{1}{6} \, \cos \left (x\right )^{6} - \frac{1}{4} \, \cos \left (x\right )^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^3*sin(x)^3,x, algorithm="giac")
[Out]