Optimal. Leaf size=21 \[ \frac{2}{7} \cos ^{\frac{7}{2}}(x)-\frac{2}{3} \cos ^{\frac{3}{2}}(x) \]
[Out]
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Rubi [A] time = 0.0356935, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{2}{7} \cos ^{\frac{7}{2}}(x)-\frac{2}{3} \cos ^{\frac{3}{2}}(x) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[Cos[x]]*Sin[x]^3,x]
[Out]
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Rubi in Sympy [A] time = 2.2582, size = 19, normalized size = 0.9 \[ \frac{2 \cos ^{\frac{7}{2}}{\left (x \right )}}{7} - \frac{2 \cos ^{\frac{3}{2}}{\left (x \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(sin(x)**3*cos(x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0343083, size = 22, normalized size = 1.05 \[ \sqrt{\cos (x)} \left (\frac{1}{14} \cos (3 x)-\frac{19 \cos (x)}{42}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[Cos[x]]*Sin[x]^3,x]
[Out]
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Maple [B] time = 0.091, size = 39, normalized size = 1.9 \[ -{\frac{8}{21}\sqrt{-2\, \left ( \sin \left ( x/2 \right ) \right ) ^{2}+1} \left ( 6\, \left ( \sin \left ( x/2 \right ) \right ) ^{6}-9\, \left ( \sin \left ( x/2 \right ) \right ) ^{4}+ \left ( \sin \left ({\frac{x}{2}} \right ) \right ) ^{2}+1 \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(sin(x)^3*cos(x)^(1/2),x)
[Out]
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Maxima [A] time = 1.36288, size = 18, normalized size = 0.86 \[ \frac{2}{7} \, \cos \left (x\right )^{\frac{7}{2}} - \frac{2}{3} \, \cos \left (x\right )^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(cos(x))*sin(x)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237176, size = 23, normalized size = 1.1 \[ \frac{2}{21} \,{\left (3 \, \cos \left (x\right )^{3} - 7 \, \cos \left (x\right )\right )} \sqrt{\cos \left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(cos(x))*sin(x)^3,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)**3*cos(x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213291, size = 18, normalized size = 0.86 \[ \frac{2}{7} \, \cos \left (x\right )^{\frac{7}{2}} - \frac{2}{3} \, \cos \left (x\right )^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(cos(x))*sin(x)^3,x, algorithm="giac")
[Out]