Optimal. Leaf size=10 \[ \frac{\tan ^{-1}\left (\frac{x}{a}\right )}{a} \]
[Out]
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Rubi [A] time = 0.00697499, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{\tan ^{-1}\left (\frac{x}{a}\right )}{a} \]
Antiderivative was successfully verified.
[In] Int[(a^2 + x^2)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 0.730526, size = 5, normalized size = 0.5 \[ \frac{\operatorname{atan}{\left (\frac{x}{a} \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a**2+x**2),x)
[Out]
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Mathematica [A] time = 0.00315407, size = 10, normalized size = 1. \[ \frac{\tan ^{-1}\left (\frac{x}{a}\right )}{a} \]
Antiderivative was successfully verified.
[In] Integrate[(a^2 + x^2)^(-1),x]
[Out]
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Maple [A] time = 0.013, size = 11, normalized size = 1.1 \[{\frac{1}{a}\arctan \left ({\frac{x}{a}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a^2+x^2),x)
[Out]
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Maxima [A] time = 1.57168, size = 14, normalized size = 1.4 \[ \frac{\arctan \left (\frac{x}{a}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a^2 + x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.19404, size = 14, normalized size = 1.4 \[ \frac{\arctan \left (\frac{x}{a}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a^2 + x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.11201, size = 20, normalized size = 2. \[ \frac{- \frac{i \log{\left (- i a + x \right )}}{2} + \frac{i \log{\left (i a + x \right )}}{2}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a**2+x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.22019, size = 14, normalized size = 1.4 \[ \frac{\arctan \left (\frac{x}{a}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a^2 + x^2),x, algorithm="giac")
[Out]