3.134 \(\int \frac{\sqrt{b x^n}}{x} \, dx\)

Optimal. Leaf size=14 \[ \frac{2 \sqrt{b x^n}}{n} \]

[Out]

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

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Rubi [A]  time = 0.00976556, antiderivative size = 14, 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 \[ \frac{2 \sqrt{b x^n}}{n} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[b*x^n]/x,x]

[Out]

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

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Rubi in Sympy [A]  time = 2.7267, size = 10, normalized size = 0.71 \[ \frac{2 \sqrt{b x^{n}}}{n} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00293232, size = 14, normalized size = 1. \[ \frac{2 \sqrt{b x^n}}{n} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[b*x^n]/x,x]

[Out]

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

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Maple [A]  time = 0.003, size = 13, normalized size = 0.9 \[ 2\,{\frac{\sqrt{b{x}^{n}}}{n}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^n)^(1/2)/x,x)

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Exception raised: ValueError

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Fricas [A]  time = 0.226632, size = 16, normalized size = 1.14 \[ \frac{2 \, \sqrt{b x^{n}}}{n} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 0.752516, size = 22, normalized size = 1.57 \[ \begin{cases} \frac{2 \sqrt{b} \sqrt{x^{n}}}{n} & \text{for}\: n \neq 0 \\\sqrt{b} \log{\left (x \right )} & \text{otherwise} \end{cases} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**n)**(1/2)/x,x)

[Out]

Piecewise((2*sqrt(b)*sqrt(x**n)/n, Ne(n, 0)), (sqrt(b)*log(x), True))

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{b x^{n}}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate(sqrt(b*x^n)/x, x)