Optimal. Leaf size=25 \[ \frac{\sin ^{10}(x)}{10}-\frac{\sin ^8(x)}{4}+\frac{\sin ^6(x)}{6} \]
[Out]
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Rubi [A] time = 0.0600106, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \frac{\sin ^{10}(x)}{10}-\frac{\sin ^8(x)}{4}+\frac{\sin ^6(x)}{6} \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^5*Sin[x]^5,x]
[Out]
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Rubi in Sympy [A] time = 3.44483, size = 19, normalized size = 0.76 \[ \frac{\sin ^{10}{\left (x \right )}}{10} - \frac{\sin ^{8}{\left (x \right )}}{4} + \frac{\sin ^{6}{\left (x \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**5*sin(x)**5,x)
[Out]
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Mathematica [A] time = 0.0156388, size = 25, normalized size = 1. \[ -\frac{5}{512} \cos (2 x)+\frac{5 \cos (6 x)}{3072}-\frac{\cos (10 x)}{5120} \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^5*Sin[x]^5,x]
[Out]
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Maple [A] time = 0.01, size = 28, normalized size = 1.1 \[ -{\frac{ \left ( \cos \left ( x \right ) \right ) ^{6} \left ( \sin \left ( x \right ) \right ) ^{4}}{10}}-{\frac{ \left ( \sin \left ( x \right ) \right ) ^{2} \left ( \cos \left ( x \right ) \right ) ^{6}}{20}}-{\frac{ \left ( \cos \left ( x \right ) \right ) ^{6}}{60}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^5*sin(x)^5,x)
[Out]
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Maxima [A] time = 1.33287, size = 26, normalized size = 1.04 \[ \frac{1}{10} \, \sin \left (x\right )^{10} - \frac{1}{4} \, \sin \left (x\right )^{8} + \frac{1}{6} \, \sin \left (x\right )^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^5*sin(x)^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230845, size = 26, normalized size = 1.04 \[ -\frac{1}{10} \, \cos \left (x\right )^{10} + \frac{1}{4} \, \cos \left (x\right )^{8} - \frac{1}{6} \, \cos \left (x\right )^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^5*sin(x)^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.053033, size = 19, normalized size = 0.76 \[ \frac{\sin ^{10}{\left (x \right )}}{10} - \frac{\sin ^{8}{\left (x \right )}}{4} + \frac{\sin ^{6}{\left (x \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**5*sin(x)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.212994, size = 26, normalized size = 1.04 \[ -\frac{1}{10} \, \cos \left (x\right )^{10} + \frac{1}{4} \, \cos \left (x\right )^{8} - \frac{1}{6} \, \cos \left (x\right )^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^5*sin(x)^5,x, algorithm="giac")
[Out]