Optimal. Leaf size=27 \[ \frac{1}{2} \left (a^2+x^2\right ) \log \left (a^2+x^2\right )-\frac{x^2}{2} \]
[Out]
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Rubi [A] time = 0.0706951, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.3 \[ \frac{1}{2} \left (a^2+x^2\right ) \log \left (a^2+x^2\right )-\frac{x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[x*Log[a^2 + x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.22678, size = 31, normalized size = 1.15 \[ \frac{a^{2} \log{\left (a^{2} + x^{2} \right )}}{2} + \frac{x^{2} \log{\left (a^{2} + x^{2} \right )}}{2} - \frac{x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*ln(a**2+x**2),x)
[Out]
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Mathematica [A] time = 0.00324879, size = 38, normalized size = 1.41 \[ \frac{1}{2} a^2 \log \left (a^2+x^2\right )+\frac{1}{2} x^2 \log \left (a^2+x^2\right )-\frac{x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[x*Log[a^2 + x^2],x]
[Out]
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Maple [A] time = 0.001, size = 29, normalized size = 1.1 \[{\frac{ \left ({a}^{2}+{x}^{2} \right ) \ln \left ({a}^{2}+{x}^{2} \right ) }{2}}-{\frac{{x}^{2}}{2}}-{\frac{{a}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*ln(a^2+x^2),x)
[Out]
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Maxima [A] time = 1.38547, size = 38, normalized size = 1.41 \[ -\frac{1}{2} \, a^{2} - \frac{1}{2} \, x^{2} + \frac{1}{2} \,{\left (a^{2} + x^{2}\right )} \log \left (a^{2} + x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*log(a^2 + x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215803, size = 31, normalized size = 1.15 \[ -\frac{1}{2} \, x^{2} + \frac{1}{2} \,{\left (a^{2} + x^{2}\right )} \log \left (a^{2} + x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*log(a^2 + x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.553694, size = 31, normalized size = 1.15 \[ \frac{a^{2} \log{\left (a^{2} + x^{2} \right )}}{2} + \frac{x^{2} \log{\left (a^{2} + x^{2} \right )}}{2} - \frac{x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*ln(a**2+x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.198737, size = 38, normalized size = 1.41 \[ -\frac{1}{2} \, a^{2} - \frac{1}{2} \, x^{2} + \frac{1}{2} \,{\left (a^{2} + x^{2}\right )}{\rm ln}\left (a^{2} + x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*log(a^2 + x^2),x, algorithm="giac")
[Out]