Optimal. Leaf size=45 \[ -\frac{64 (3-8 x)}{243 \sqrt{3 x-4 x^2}}-\frac{2 (3-8 x)}{27 \left (3 x-4 x^2\right )^{3/2}} \]
[Out]
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Rubi [A] time = 0.0202536, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{64 (3-8 x)}{243 \sqrt{3 x-4 x^2}}-\frac{2 (3-8 x)}{27 \left (3 x-4 x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[(3*x - 4*x^2)^(-5/2),x]
[Out]
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Rubi in Sympy [A] time = 1.61603, size = 37, normalized size = 0.82 \[ - \frac{32 \left (- 16 x + 6\right )}{243 \sqrt{- 4 x^{2} + 3 x}} - \frac{2 \left (- 8 x + 3\right )}{27 \left (- 4 x^{2} + 3 x\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-4*x**2+3*x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0230932, size = 31, normalized size = 0.69 \[ -\frac{2048 x^3-2304 x^2+432 x+54}{243 (-x (4 x-3))^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(3*x - 4*x^2)^(-5/2),x]
[Out]
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Maple [A] time = 0.004, size = 35, normalized size = 0.8 \[{\frac{2\,x \left ( 4\,x-3 \right ) \left ( 1024\,{x}^{3}-1152\,{x}^{2}+216\,x+27 \right ) }{243} \left ( -4\,{x}^{2}+3\,x \right ) ^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-4*x^2+3*x)^(5/2),x)
[Out]
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Maxima [A] time = 0.689655, size = 74, normalized size = 1.64 \[ \frac{512 \, x}{243 \, \sqrt{-4 \, x^{2} + 3 \, x}} - \frac{64}{81 \, \sqrt{-4 \, x^{2} + 3 \, x}} + \frac{16 \, x}{27 \,{\left (-4 \, x^{2} + 3 \, x\right )}^{\frac{3}{2}}} - \frac{2}{9 \,{\left (-4 \, x^{2} + 3 \, x\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-4*x^2 + 3*x)^(-5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216312, size = 53, normalized size = 1.18 \[ \frac{2 \,{\left (1024 \, x^{3} - 1152 \, x^{2} + 216 \, x + 27\right )}}{243 \,{\left (4 \, x^{2} - 3 \, x\right )} \sqrt{-4 \, x^{2} + 3 \, x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-4*x^2 + 3*x)^(-5/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (- 4 x^{2} + 3 x\right )^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-4*x**2+3*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.219204, size = 53, normalized size = 1.18 \[ -\frac{2 \,{\left (8 \,{\left (16 \,{\left (8 \, x - 9\right )} x + 27\right )} x + 27\right )} \sqrt{-4 \, x^{2} + 3 \, x}}{243 \,{\left (4 \, x^{2} - 3 \, x\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-4*x^2 + 3*x)^(-5/2),x, algorithm="giac")
[Out]