Optimal. Leaf size=25 \[ \frac{\left (b x^2+c x^4\right )^{3/2}}{3 c x^3} \]
[Out]
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Rubi [A] time = 0.0159563, antiderivative size = 25, 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 \[ \frac{\left (b x^2+c x^4\right )^{3/2}}{3 c x^3} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b*x^2 + c*x^4],x]
[Out]
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Rubi in Sympy [A] time = 5.1575, size = 19, normalized size = 0.76 \[ \frac{\left (b x^{2} + c x^{4}\right )^{\frac{3}{2}}}{3 c x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00956013, size = 25, normalized size = 1. \[ \frac{\left (x^2 \left (b+c x^2\right )\right )^{3/2}}{3 c x^3} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b*x^2 + c*x^4],x]
[Out]
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Maple [A] time = 0.004, size = 29, normalized size = 1.2 \[{\frac{c{x}^{2}+b}{3\,cx}\sqrt{c{x}^{4}+b{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2)^(1/2),x)
[Out]
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Maxima [A] time = 0.701052, size = 19, normalized size = 0.76 \[ \frac{{\left (c x^{2} + b\right )}^{\frac{3}{2}}}{3 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^4 + b*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.259146, size = 38, normalized size = 1.52 \[ \frac{\sqrt{c x^{4} + b x^{2}}{\left (c x^{2} + b\right )}}{3 \, c x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^4 + b*x^2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{b x^{2} + c x^{4}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.270496, size = 36, normalized size = 1.44 \[ \frac{{\left (c x^{2} + b\right )}^{\frac{3}{2}}{\rm sign}\left (x\right )}{3 \, c} - \frac{b^{\frac{3}{2}}{\rm sign}\left (x\right )}{3 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^4 + b*x^2),x, algorithm="giac")
[Out]