3.6 \(\int \frac{\sqrt{b x^2}}{x} \, dx\)

Optimal. Leaf size=9 \[ \sqrt{b x^2} \]

[Out]

Sqrt[b*x^2]

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Rubi [A]  time = 0.00514821, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[b*x^2]/x,x]

[Out]

Sqrt[b*x^2]

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Rubi in Sympy [A]  time = 2.27226, size = 7, normalized size = 0.78 \[ \sqrt{b x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(1/2)/x,x)

[Out]

sqrt(b*x**2)

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Mathematica [A]  time = 0.0033611, size = 14, normalized size = 1.56 \[ \frac{b x^2}{\sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[b*x^2]/x,x]

[Out]

(b*x^2)/Sqrt[b*x^2]

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Maple [A]  time = 0.002, size = 8, normalized size = 0.9 \[ \sqrt{b{x}^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(1/2)/x,x)

[Out]

(b*x^2)^(1/2)

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b*x^2)/x,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.234135, size = 9, normalized size = 1. \[ \sqrt{b x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b*x^2)/x,x, algorithm="fricas")

[Out]

sqrt(b*x^2)

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Sympy [A]  time = 0.390247, size = 10, normalized size = 1.11 \[ \sqrt{b} \sqrt{x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(1/2)/x,x)

[Out]

sqrt(b)*sqrt(x**2)

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GIAC/XCAS [A]  time = 0.207244, size = 9, normalized size = 1. \[ \sqrt{b} x{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b*x^2)/x,x, algorithm="giac")

[Out]

sqrt(b)*x*sign(x)