3.53 \(\int x^5 \cos \left (x^3\right ) \, dx\)

Optimal. Leaf size=20 \[ \frac{1}{3} x^3 \sin \left (x^3\right )+\frac{\cos \left (x^3\right )}{3} \]

[Out]

Cos[x^3]/3 + (x^3*Sin[x^3])/3

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Rubi [A]  time = 0.0255628, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375 \[ \frac{1}{3} x^3 \sin \left (x^3\right )+\frac{\cos \left (x^3\right )}{3} \]

Antiderivative was successfully verified.

[In]  Int[x^5*Cos[x^3],x]

[Out]

Cos[x^3]/3 + (x^3*Sin[x^3])/3

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Rubi in Sympy [A]  time = 1.44231, size = 15, normalized size = 0.75 \[ \frac{x^{3} \sin{\left (x^{3} \right )}}{3} + \frac{\cos{\left (x^{3} \right )}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**5*cos(x**3),x)

[Out]

x**3*sin(x**3)/3 + cos(x**3)/3

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Mathematica [A]  time = 0.00490662, size = 20, normalized size = 1. \[ \frac{1}{3} x^3 \sin \left (x^3\right )+\frac{\cos \left (x^3\right )}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[x^5*Cos[x^3],x]

[Out]

Cos[x^3]/3 + (x^3*Sin[x^3])/3

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Maple [A]  time = 0.009, size = 17, normalized size = 0.9 \[{\frac{\cos \left ({x}^{3} \right ) }{3}}+{\frac{{x}^{3}\sin \left ({x}^{3} \right ) }{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^5*cos(x^3),x)

[Out]

1/3*cos(x^3)+1/3*x^3*sin(x^3)

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Maxima [A]  time = 1.34878, size = 22, normalized size = 1.1 \[ \frac{1}{3} \, x^{3} \sin \left (x^{3}\right ) + \frac{1}{3} \, \cos \left (x^{3}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5*cos(x^3),x, algorithm="maxima")

[Out]

1/3*x^3*sin(x^3) + 1/3*cos(x^3)

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Fricas [A]  time = 0.21938, size = 22, normalized size = 1.1 \[ \frac{1}{3} \, x^{3} \sin \left (x^{3}\right ) + \frac{1}{3} \, \cos \left (x^{3}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5*cos(x^3),x, algorithm="fricas")

[Out]

1/3*x^3*sin(x^3) + 1/3*cos(x^3)

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Sympy [A]  time = 2.95039, size = 15, normalized size = 0.75 \[ \frac{x^{3} \sin{\left (x^{3} \right )}}{3} + \frac{\cos{\left (x^{3} \right )}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**5*cos(x**3),x)

[Out]

x**3*sin(x**3)/3 + cos(x**3)/3

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GIAC/XCAS [A]  time = 0.199178, size = 22, normalized size = 1.1 \[ \frac{1}{3} \, x^{3} \sin \left (x^{3}\right ) + \frac{1}{3} \, \cos \left (x^{3}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5*cos(x^3),x, algorithm="giac")

[Out]

1/3*x^3*sin(x^3) + 1/3*cos(x^3)