Optimal. Leaf size=19 \[ \frac{2 x}{b \sqrt{b x+c x^2}} \]
[Out]
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Rubi [A] time = 0.0248089, antiderivative size = 19, 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 \[ \frac{2 x}{b \sqrt{b x+c x^2}} \]
Antiderivative was successfully verified.
[In] Int[x/(b*x + c*x^2)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 3.24221, size = 15, normalized size = 0.79 \[ \frac{2 x}{b \sqrt{b x + c x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(c*x**2+b*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0153441, size = 17, normalized size = 0.89 \[ \frac{2 x}{b \sqrt{x (b+c x)}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(b*x + c*x^2)^(3/2),x]
[Out]
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Maple [A] time = 0.006, size = 25, normalized size = 1.3 \[ 2\,{\frac{{x}^{2} \left ( cx+b \right ) }{b \left ( c{x}^{2}+bx \right ) ^{3/2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(c*x^2+b*x)^(3/2),x)
[Out]
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Maxima [A] time = 0.707546, size = 23, normalized size = 1.21 \[ \frac{2 \, x}{\sqrt{c x^{2} + b x} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(c*x^2 + b*x)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217289, size = 23, normalized size = 1.21 \[ \frac{2 \, x}{\sqrt{c x^{2} + b x} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(c*x^2 + b*x)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x}{\left (x \left (b + c x\right )\right )^{\frac{3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(c*x**2+b*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.220794, size = 43, normalized size = 2.26 \[ \frac{2}{{\left ({\left (\sqrt{c} x - \sqrt{c x^{2} + b x}\right )} \sqrt{c} + b\right )} \sqrt{c}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(c*x^2 + b*x)^(3/2),x, algorithm="giac")
[Out]