3.54 \(\int x \cos \left (x^2\right ) \sin \left (x^2\right ) \, dx\)

Optimal. Leaf size=10 \[ \frac{1}{4} \sin ^2\left (x^2\right ) \]

[Out]

Sin[x^2]^2/4

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Rubi [A]  time = 0.0129177, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{1}{4} \sin ^2\left (x^2\right ) \]

Antiderivative was successfully verified.

[In]  Int[x*Cos[x^2]*Sin[x^2],x]

[Out]

Sin[x^2]^2/4

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Rubi in Sympy [A]  time = 0.993824, size = 7, normalized size = 0.7 \[ \frac{\sin ^{2}{\left (x^{2} \right )}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x*cos(x**2)*sin(x**2),x)

[Out]

sin(x**2)**2/4

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Mathematica [A]  time = 0.00431081, size = 10, normalized size = 1. \[ -\frac{1}{4} \cos ^2\left (x^2\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x*Cos[x^2]*Sin[x^2],x]

[Out]

-Cos[x^2]^2/4

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Maple [A]  time = 0.003, size = 9, normalized size = 0.9 \[ -{\frac{ \left ( \cos \left ({x}^{2} \right ) \right ) ^{2}}{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*cos(x^2)*sin(x^2),x)

[Out]

-1/4*cos(x^2)^2

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Maxima [A]  time = 1.35312, size = 11, normalized size = 1.1 \[ -\frac{1}{4} \, \cos \left (x^{2}\right )^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*cos(x^2)*sin(x^2),x, algorithm="maxima")

[Out]

-1/4*cos(x^2)^2

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Fricas [A]  time = 0.249941, size = 11, normalized size = 1.1 \[ -\frac{1}{4} \, \cos \left (x^{2}\right )^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*cos(x^2)*sin(x^2),x, algorithm="fricas")

[Out]

-1/4*cos(x^2)^2

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Sympy [A]  time = 0.360121, size = 7, normalized size = 0.7 \[ \frac{\sin ^{2}{\left (x^{2} \right )}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*cos(x**2)*sin(x**2),x)

[Out]

sin(x**2)**2/4

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GIAC/XCAS [A]  time = 0.224803, size = 11, normalized size = 1.1 \[ -\frac{1}{4} \, \cos \left (x^{2}\right )^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*cos(x^2)*sin(x^2),x, algorithm="giac")

[Out]

-1/4*cos(x^2)^2