Optimal. Leaf size=33 \[ \frac{\cos ^{13}(x)}{13}-\frac{3 \cos ^{11}(x)}{11}+\frac{\cos ^9(x)}{3}-\frac{\cos ^7(x)}{7} \]
[Out]
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Rubi [A] time = 0.0555727, antiderivative size = 33, 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 \[ \frac{\cos ^{13}(x)}{13}-\frac{3 \cos ^{11}(x)}{11}+\frac{\cos ^9(x)}{3}-\frac{\cos ^7(x)}{7} \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^6*Sin[x]^7,x]
[Out]
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Rubi in Sympy [A] time = 3.256, size = 27, normalized size = 0.82 \[ \frac{\cos ^{13}{\left (x \right )}}{13} - \frac{3 \cos ^{11}{\left (x \right )}}{11} + \frac{\cos ^{9}{\left (x \right )}}{3} - \frac{\cos ^{7}{\left (x \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**6*sin(x)**7,x)
[Out]
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Mathematica [A] time = 0.034187, size = 55, normalized size = 1.67 \[ -\frac{5 \cos (x)}{1024}-\frac{5 \cos (3 x)}{4096}+\frac{3 \cos (5 x)}{4096}+\frac{3 \cos (7 x)}{14336}-\frac{\cos (9 x)}{6144}-\frac{\cos (11 x)}{45056}+\frac{\cos (13 x)}{53248} \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^6*Sin[x]^7,x]
[Out]
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Maple [A] time = 0.012, size = 38, normalized size = 1.2 \[ -{\frac{ \left ( \cos \left ( x \right ) \right ) ^{7} \left ( \sin \left ( x \right ) \right ) ^{6}}{13}}-{\frac{6\, \left ( \sin \left ( x \right ) \right ) ^{4} \left ( \cos \left ( x \right ) \right ) ^{7}}{143}}-{\frac{8\, \left ( \sin \left ( x \right ) \right ) ^{2} \left ( \cos \left ( x \right ) \right ) ^{7}}{429}}-{\frac{16\, \left ( \cos \left ( x \right ) \right ) ^{7}}{3003}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^6*sin(x)^7,x)
[Out]
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Maxima [A] time = 1.42244, size = 34, normalized size = 1.03 \[ \frac{1}{13} \, \cos \left (x\right )^{13} - \frac{3}{11} \, \cos \left (x\right )^{11} + \frac{1}{3} \, \cos \left (x\right )^{9} - \frac{1}{7} \, \cos \left (x\right )^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^6*sin(x)^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234401, size = 34, normalized size = 1.03 \[ \frac{1}{13} \, \cos \left (x\right )^{13} - \frac{3}{11} \, \cos \left (x\right )^{11} + \frac{1}{3} \, \cos \left (x\right )^{9} - \frac{1}{7} \, \cos \left (x\right )^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^6*sin(x)^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.052812, size = 27, normalized size = 0.82 \[ \frac{\cos ^{13}{\left (x \right )}}{13} - \frac{3 \cos ^{11}{\left (x \right )}}{11} + \frac{\cos ^{9}{\left (x \right )}}{3} - \frac{\cos ^{7}{\left (x \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**6*sin(x)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.202166, size = 34, normalized size = 1.03 \[ \frac{1}{13} \, \cos \left (x\right )^{13} - \frac{3}{11} \, \cos \left (x\right )^{11} + \frac{1}{3} \, \cos \left (x\right )^{9} - \frac{1}{7} \, \cos \left (x\right )^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^6*sin(x)^7,x, algorithm="giac")
[Out]