Optimal. Leaf size=26 \[ \frac{\sin (a+b x)}{b}-\frac{\sin ^3(a+b x)}{3 b} \]
[Out]
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Rubi [A] time = 0.0208488, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{\sin (a+b x)}{b}-\frac{\sin ^3(a+b x)}{3 b} \]
Antiderivative was successfully verified.
[In] Int[Cos[a + b*x]^3,x]
[Out]
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Rubi in Sympy [A] time = 1.13957, size = 19, normalized size = 0.73 \[ - \frac{\sin ^{3}{\left (a + b x \right )}}{3 b} + \frac{\sin{\left (a + b x \right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(b*x+a)**3,x)
[Out]
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Mathematica [A] time = 0.00946222, size = 29, normalized size = 1.12 \[ \frac{3 \sin (a+b x)}{4 b}+\frac{\sin (3 (a+b x))}{12 b} \]
Antiderivative was successfully verified.
[In] Integrate[Cos[a + b*x]^3,x]
[Out]
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Maple [A] time = 0.004, size = 22, normalized size = 0.9 \[{\frac{ \left ( 2+ \left ( \cos \left ( bx+a \right ) \right ) ^{2} \right ) \sin \left ( bx+a \right ) }{3\,b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(b*x+a)^3,x)
[Out]
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Maxima [A] time = 1.38757, size = 30, normalized size = 1.15 \[ -\frac{\sin \left (b x + a\right )^{3} - 3 \, \sin \left (b x + a\right )}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(b*x + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223909, size = 28, normalized size = 1.08 \[ \frac{{\left (\cos \left (b x + a\right )^{2} + 2\right )} \sin \left (b x + a\right )}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(b*x + a)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.608875, size = 36, normalized size = 1.38 \[ \begin{cases} \frac{2 \sin ^{3}{\left (a + b x \right )}}{3 b} + \frac{\sin{\left (a + b x \right )} \cos ^{2}{\left (a + b x \right )}}{b} & \text{for}\: b \neq 0 \\x \cos ^{3}{\left (a \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(b*x+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.201955, size = 30, normalized size = 1.15 \[ -\frac{\sin \left (b x + a\right )^{3} - 3 \, \sin \left (b x + a\right )}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(b*x + a)^3,x, algorithm="giac")
[Out]