Optimal. Leaf size=16 \[ \frac{1}{2} i \sin ^{-1}\left (1-\frac{8 i x}{3}\right ) \]
[Out]
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Rubi [A] time = 0.0159438, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{1}{2} i \sin ^{-1}\left (1-\frac{8 i x}{3}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[(3*I)*x + 4*x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.36067, size = 8, normalized size = 0.5 \[ \frac{\operatorname{asinh}{\left (\frac{8 x}{3} + i \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(3*I*x+4*x**2)**(1/2),x)
[Out]
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Mathematica [B] time = 0.0178141, size = 50, normalized size = 3.12 \[ \frac{\sqrt{x} \sqrt{4 x+3 i} \log \left (2 \sqrt{x}+\sqrt{4 x+3 i}\right )}{\sqrt{x (4 x+3 i)}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[(3*I)*x + 4*x^2],x]
[Out]
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Maple [A] time = 0.01, size = 10, normalized size = 0.6 \[{\frac{1}{2}{\it Arcsinh} \left ({\frac{8\,x}{3}}+i \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(3*I*x+4*x^2)^(1/2),x)
[Out]
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Maxima [A] time = 0.792402, size = 28, normalized size = 1.75 \[ \frac{1}{2} \, \log \left (8 \, x + 4 \, \sqrt{4 \, x^{2} + 3 i \, x} + 3 i\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(4*x^2 + 3*I*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212793, size = 26, normalized size = 1.62 \[ -\frac{1}{2} \, \log \left (-2 \, x + \sqrt{4 \, x^{2} + 3 i \, x} - \frac{3}{4} i\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(4*x^2 + 3*I*x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{4 x^{2} + 3 i x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3*I*x+4*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(4*x^2 + 3*I*x),x, algorithm="giac")
[Out]