3.2 \(\int \frac{1}{1+x^2} \, dx\)

Optimal. Leaf size=2 \[ \tan ^{-1}(x) \]

[Out]

ArcTan[x]

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Rubi [A]  time = 0.00344078, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \tan ^{-1}(x) \]

Antiderivative was successfully verified.

[In]  Int[(1 + x^2)^(-1),x]

[Out]

ArcTan[x]

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Rubi in Sympy [A]  time = 0.062405, size = 2, normalized size = 1. \[ \operatorname{atan}{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(x**2+1),x)

[Out]

atan(x)

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Mathematica [A]  time = 0.00354925, size = 2, normalized size = 1. \[ \tan ^{-1}(x) \]

Antiderivative was successfully verified.

[In]  Integrate[(1 + x^2)^(-1),x]

[Out]

ArcTan[x]

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Maple [A]  time = 0.001, size = 3, normalized size = 1.5 \[ \arctan \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(x^2+1),x)

[Out]

arctan(x)

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Maxima [A]  time = 1.55801, size = 3, normalized size = 1.5 \[ \arctan \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(x^2 + 1),x, algorithm="maxima")

[Out]

arctan(x)

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Fricas [A]  time = 0.19266, size = 3, normalized size = 1.5 \[ \arctan \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(x^2 + 1),x, algorithm="fricas")

[Out]

arctan(x)

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Sympy [A]  time = 0.072085, size = 2, normalized size = 1. \[ \operatorname{atan}{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(x**2+1),x)

[Out]

atan(x)

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GIAC/XCAS [A]  time = 0.19615, size = 3, normalized size = 1.5 \[ \arctan \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(x^2 + 1),x, algorithm="giac")

[Out]

arctan(x)