Optimal. Leaf size=26 \[ \frac{2 (8 x+3 i)}{9 \sqrt{4 x^2+3 i x}} \]
[Out]
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Rubi [A] time = 0.0101403, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{2 (8 x+3 i)}{9 \sqrt{4 x^2+3 i x}} \]
Antiderivative was successfully verified.
[In] Int[((3*I)*x + 4*x^2)^(-3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.27876, size = 20, normalized size = 0.77 \[ \frac{16 x + 6 i}{9 \sqrt{4 x^{2} + 3 i x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(3*I*x+4*x**2)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0153368, size = 24, normalized size = 0.92 \[ \frac{2 (8 x+3 i)}{9 \sqrt{x (4 x+3 i)}} \]
Antiderivative was successfully verified.
[In] Integrate[((3*I)*x + 4*x^2)^(-3/2),x]
[Out]
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Maple [A] time = 0.01, size = 21, normalized size = 0.8 \[{\frac{6\,i+16\,x}{9}{\frac{1}{\sqrt{3\,ix+4\,{x}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(3*I*x+4*x^2)^(3/2),x)
[Out]
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Maxima [A] time = 0.711006, size = 38, normalized size = 1.46 \[ \frac{16 \, x}{9 \, \sqrt{4 \, x^{2} + 3 i \, x}} + \frac{2 i}{3 \, \sqrt{4 \, x^{2} + 3 i \, x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 + 3*I*x)^(-3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212089, size = 42, normalized size = 1.62 \[ \frac{2}{16 \, x^{2} - \sqrt{4 \, x^{2} + 3 i \, x}{\left (8 \, x + 3 i\right )} + 12 i \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 + 3*I*x)^(-3/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (4 x^{2} + 3 i x\right )^{\frac{3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3*I*x+4*x**2)**(3/2),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((4*x^2 + 3*I*x)^(-3/2),x, algorithm="giac")
[Out]