Optimal. Leaf size=25 \[ \frac{2 \left (a x^2+b x^3\right )^{3/2}}{3 b x^3} \]
[Out]
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Rubi [A] time = 0.0654432, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{2 \left (a x^2+b x^3\right )^{3/2}}{3 b x^3} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a*x^2 + b*x^3]/x,x]
[Out]
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Rubi in Sympy [A] time = 7.50002, size = 20, normalized size = 0.8 \[ \frac{2 \left (a x^{2} + b x^{3}\right )^{\frac{3}{2}}}{3 b x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a*x**2)**(1/2)/x,x)
[Out]
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Mathematica [A] time = 0.0172141, size = 23, normalized size = 0.92 \[ \frac{2 \left (x^2 (a+b x)\right )^{3/2}}{3 b x^3} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a*x^2 + b*x^3]/x,x]
[Out]
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Maple [A] time = 0.003, size = 27, normalized size = 1.1 \[{\frac{2\,bx+2\,a}{3\,bx}\sqrt{b{x}^{3}+a{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a*x^2)^(1/2)/x,x)
[Out]
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Maxima [A] time = 1.41592, size = 16, normalized size = 0.64 \[ \frac{2 \,{\left (b x + a\right )}^{\frac{3}{2}}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^3 + a*x^2)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224671, size = 35, normalized size = 1.4 \[ \frac{2 \, \sqrt{b x^{3} + a x^{2}}{\left (b x + a\right )}}{3 \, b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^3 + a*x^2)/x,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x^{2} \left (a + b x\right )}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a*x**2)**(1/2)/x,x)
[Out]
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GIAC/XCAS [A] time = 0.218038, size = 34, normalized size = 1.36 \[ \frac{2 \,{\left (b x + a\right )}^{\frac{3}{2}}{\rm sign}\left (x\right )}{3 \, b} - \frac{2 \, a^{\frac{3}{2}}{\rm sign}\left (x\right )}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^3 + a*x^2)/x,x, algorithm="giac")
[Out]