Optimal. Leaf size=25 \[ \frac{2 \left (b x+c x^2\right )^{3/2}}{3 c x^{3/2}} \]
[Out]
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Rubi [A] time = 0.0263756, 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 \[ \frac{2 \left (b x+c x^2\right )^{3/2}}{3 c x^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b*x + c*x^2]/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 3.61731, size = 20, normalized size = 0.8 \[ \frac{2 \left (b x + c x^{2}\right )^{\frac{3}{2}}}{3 c x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+b*x)**(1/2)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0191625, size = 23, normalized size = 0.92 \[ \frac{2 (x (b+c x))^{3/2}}{3 c x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b*x + c*x^2]/Sqrt[x],x]
[Out]
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Maple [A] time = 0.006, size = 25, normalized size = 1. \[{\frac{2\,cx+2\,b}{3\,c}\sqrt{c{x}^{2}+bx}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+b*x)^(1/2)/x^(1/2),x)
[Out]
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Maxima [A] time = 0.717153, size = 16, normalized size = 0.64 \[ \frac{2 \,{\left (c x + b\right )}^{\frac{3}{2}}}{3 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2 + b*x)/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222882, size = 53, normalized size = 2.12 \[ \frac{2 \,{\left (c^{2} x^{3} + 2 \, b c x^{2} + b^{2} x\right )}}{3 \, \sqrt{c x^{2} + b x} c \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2 + b*x)/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x \left (b + c x\right )}}{\sqrt{x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+b*x)**(1/2)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.208015, size = 28, normalized size = 1.12 \[ \frac{2 \,{\left (c x + b\right )}^{\frac{3}{2}}}{3 \, c} - \frac{2 \, b^{\frac{3}{2}}}{3 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2 + b*x)/sqrt(x),x, algorithm="giac")
[Out]