Optimal. Leaf size=44 \[ \frac{35 x}{128}-\frac{1}{8} \sin ^7(x) \cos (x)-\frac{7}{48} \sin ^5(x) \cos (x)-\frac{35}{192} \sin ^3(x) \cos (x)-\frac{35}{128} \sin (x) \cos (x) \]
[Out]
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Rubi [A] time = 0.0390427, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ \frac{35 x}{128}-\frac{1}{8} \sin ^7(x) \cos (x)-\frac{7}{48} \sin ^5(x) \cos (x)-\frac{35}{192} \sin ^3(x) \cos (x)-\frac{35}{128} \sin (x) \cos (x) \]
Antiderivative was successfully verified.
[In] Int[Sin[x]^8,x]
[Out]
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Rubi in Sympy [A] time = 0.801034, size = 48, normalized size = 1.09 \[ \frac{35 x}{128} - \frac{\sin ^{7}{\left (x \right )} \cos{\left (x \right )}}{8} - \frac{7 \sin ^{5}{\left (x \right )} \cos{\left (x \right )}}{48} - \frac{35 \sin ^{3}{\left (x \right )} \cos{\left (x \right )}}{192} - \frac{35 \sin{\left (x \right )} \cos{\left (x \right )}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(sin(x)**8,x)
[Out]
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Mathematica [A] time = 0.00329582, size = 38, normalized size = 0.86 \[ \frac{35 x}{128}-\frac{7}{32} \sin (2 x)+\frac{7}{128} \sin (4 x)-\frac{1}{96} \sin (6 x)+\frac{\sin (8 x)}{1024} \]
Antiderivative was successfully verified.
[In] Integrate[Sin[x]^8,x]
[Out]
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Maple [A] time = 0.053, size = 30, normalized size = 0.7 \[ -{\frac{\cos \left ( x \right ) }{8} \left ( \left ( \sin \left ( x \right ) \right ) ^{7}+{\frac{7\, \left ( \sin \left ( x \right ) \right ) ^{5}}{6}}+{\frac{35\, \left ( \sin \left ( x \right ) \right ) ^{3}}{24}}+{\frac{35\,\sin \left ( x \right ) }{16}} \right ) }+{\frac{35\,x}{128}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(sin(x)^8,x)
[Out]
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Maxima [A] time = 1.35111, size = 41, normalized size = 0.93 \[ \frac{1}{24} \, \sin \left (2 \, x\right )^{3} + \frac{35}{128} \, x + \frac{1}{1024} \, \sin \left (8 \, x\right ) + \frac{7}{128} \, \sin \left (4 \, x\right ) - \frac{1}{4} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228707, size = 42, normalized size = 0.95 \[ \frac{1}{384} \,{\left (48 \, \cos \left (x\right )^{7} - 200 \, \cos \left (x\right )^{5} + 326 \, \cos \left (x\right )^{3} - 279 \, \cos \left (x\right )\right )} \sin \left (x\right ) + \frac{35}{128} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.041714, size = 48, normalized size = 1.09 \[ \frac{35 x}{128} - \frac{\sin ^{7}{\left (x \right )} \cos{\left (x \right )}}{8} - \frac{7 \sin ^{5}{\left (x \right )} \cos{\left (x \right )}}{48} - \frac{35 \sin ^{3}{\left (x \right )} \cos{\left (x \right )}}{192} - \frac{35 \sin{\left (x \right )} \cos{\left (x \right )}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.199166, size = 38, normalized size = 0.86 \[ \frac{35}{128} \, x + \frac{1}{1024} \, \sin \left (8 \, x\right ) - \frac{1}{96} \, \sin \left (6 \, x\right ) + \frac{7}{128} \, \sin \left (4 \, x\right ) - \frac{7}{32} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^8,x, algorithm="giac")
[Out]