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

Optimal. Leaf size=13 \[ \frac{x^2}{\sqrt{b x^2}} \]

[Out]

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

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Rubi [A]  time = 0.00611616, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{x^2}{\sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[x/Sqrt[b*x^2],x]

[Out]

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

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Rubi in Sympy [A]  time = 2.21755, size = 8, normalized size = 0.62 \[ \frac{\sqrt{b x^{2}}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sqrt(b*x**2)/b

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Mathematica [A]  time = 0.00177911, size = 13, normalized size = 1. \[ \frac{x^2}{\sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x/Sqrt[b*x^2],x]

[Out]

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

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Maple [A]  time = 0.003, size = 12, normalized size = 0.9 \[{{x}^{2}{\frac{1}{\sqrt{b{x}^{2}}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/(b*x^2)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.43337, size = 15, normalized size = 1.15 \[ \frac{\sqrt{b x^{2}}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sqrt(b*x^2)/b

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Fricas [A]  time = 0.219946, size = 15, normalized size = 1.15 \[ \frac{\sqrt{b x^{2}}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sqrt(b*x^2)/b

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Sympy [A]  time = 1.63737, size = 14, normalized size = 1.08 \[ \frac{x^{2}}{\sqrt{b} \sqrt{x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(b*x**2)**(1/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.213015, size = 15, normalized size = 1.15 \[ \frac{\sqrt{b x^{2}}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sqrt(b*x^2)/b