Optimal. Leaf size=17 \[ \frac{\cos ^7(x)}{7}-\frac{\cos ^5(x)}{5} \]
[Out]
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Rubi [A] time = 0.0360282, 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 \[ \frac{\cos ^7(x)}{7}-\frac{\cos ^5(x)}{5} \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^4*Sin[x]^3,x]
[Out]
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Rubi in Sympy [A] time = 2.33001, size = 12, normalized size = 0.71 \[ \frac{\cos ^{7}{\left (x \right )}}{7} - \frac{\cos ^{5}{\left (x \right )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**4*sin(x)**3,x)
[Out]
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Mathematica [A] time = 0.0157803, size = 31, normalized size = 1.82 \[ -\frac{3 \cos (x)}{64}-\frac{1}{64} \cos (3 x)+\frac{1}{320} \cos (5 x)+\frac{1}{448} \cos (7 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^4*Sin[x]^3,x]
[Out]
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Maple [A] time = 0.01, size = 18, normalized size = 1.1 \[ -{\frac{ \left ( \cos \left ( x \right ) \right ) ^{5} \left ( \sin \left ( x \right ) \right ) ^{2}}{7}}-{\frac{2\, \left ( \cos \left ( x \right ) \right ) ^{5}}{35}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^4*sin(x)^3,x)
[Out]
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Maxima [A] time = 1.32518, size = 18, normalized size = 1.06 \[ \frac{1}{7} \, \cos \left (x\right )^{7} - \frac{1}{5} \, \cos \left (x\right )^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4*sin(x)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221402, size = 18, normalized size = 1.06 \[ \frac{1}{7} \, \cos \left (x\right )^{7} - \frac{1}{5} \, \cos \left (x\right )^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4*sin(x)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.05273, size = 12, normalized size = 0.71 \[ \frac{\cos ^{7}{\left (x \right )}}{7} - \frac{\cos ^{5}{\left (x \right )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**4*sin(x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.201719, size = 18, normalized size = 1.06 \[ \frac{1}{7} \, \cos \left (x\right )^{7} - \frac{1}{5} \, \cos \left (x\right )^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4*sin(x)^3,x, algorithm="giac")
[Out]