Optimal. Leaf size=23 \[ -\frac{2 \left (b x+c x^2\right )^{3/2}}{3 b x^3} \]
[Out]
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Rubi [A] time = 0.0288125, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{2 \left (b x+c x^2\right )^{3/2}}{3 b x^3} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b*x + c*x^2]/x^3,x]
[Out]
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Rubi in Sympy [A] time = 3.7221, size = 20, normalized size = 0.87 \[ - \frac{2 \left (b x + c x^{2}\right )^{\frac{3}{2}}}{3 b x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+b*x)**(1/2)/x**3,x)
[Out]
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Mathematica [A] time = 0.0211637, size = 21, normalized size = 0.91 \[ -\frac{2 (x (b+c x))^{3/2}}{3 b x^3} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b*x + c*x^2]/x^3,x]
[Out]
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Maple [A] time = 0.006, size = 25, normalized size = 1.1 \[ -{\frac{2\,cx+2\,b}{3\,b{x}^{2}}\sqrt{c{x}^{2}+bx}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+b*x)^(1/2)/x^3,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2 + b*x)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220299, size = 32, normalized size = 1.39 \[ -\frac{2 \, \sqrt{c x^{2} + b x}{\left (c x + b\right )}}{3 \, b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2 + b*x)/x^3,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x \left (b + c x\right )}}{x^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+b*x)**(1/2)/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.212049, size = 103, normalized size = 4.48 \[ \frac{2 \,{\left (3 \,{\left (\sqrt{c} x - \sqrt{c x^{2} + b x}\right )}^{2} c + 3 \,{\left (\sqrt{c} x - \sqrt{c x^{2} + b x}\right )} b \sqrt{c} + b^{2}\right )}}{3 \,{\left (\sqrt{c} x - \sqrt{c x^{2} + b x}\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2 + b*x)/x^3,x, algorithm="giac")
[Out]