3.1.91 \(\int \frac {1}{\sqrt {b x}} \, dx\) [91]

Optimal. Leaf size=12 \[ \frac {2 \sqrt {b x}}{b} \]

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32} \begin {gather*} \frac {2 \sqrt {b x}}{b} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1/Sqrt[b*x],x]

[Out]

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

Rule 32

Int[((a_.) + (b_.)*(x_))^(m_), x_Symbol] :> Simp[(a + b*x)^(m + 1)/(b*(m + 1)), x] /; FreeQ[{a, b, m}, x] && N
eQ[m, -1]

Rubi steps

\begin {align*} \int \frac {1}{\sqrt {b x}} \, dx &=\frac {2 \sqrt {b x}}{b}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} \frac {2 x}{\sqrt {b x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1/Sqrt[b*x],x]

[Out]

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

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Maple [A]
time = 0.02, size = 11, normalized size = 0.92

method	result	size
gosper	\(\frac {2 x}{\sqrt {b x}}\)	\(9\)
risch	\(\frac {2 x}{\sqrt {b x}}\)	\(9\)
derivativedivides	\(\frac {2 \sqrt {b x}}{b}\)	\(11\)
default	\(\frac {2 \sqrt {b x}}{b}\)	\(11\)
trager	\(\frac {2 \sqrt {b x}}{b}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(b*x)^(1/2),x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.27, size = 10, normalized size = 0.83 \begin {gather*} \frac {2 \, \sqrt {b x}}{b} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(b*x)^(1/2),x, algorithm="maxima")

[Out]

2*sqrt(b*x)/b

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Fricas [A]
time = 0.33, size = 10, normalized size = 0.83 \begin {gather*} \frac {2 \, \sqrt {b x}}{b} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(b*x)^(1/2),x, algorithm="fricas")

[Out]

2*sqrt(b*x)/b

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Sympy [A]
time = 0.01, size = 8, normalized size = 0.67 \begin {gather*} \frac {2 \sqrt {b x}}{b} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(b*x)**(1/2),x)

[Out]

2*sqrt(b*x)/b

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Giac [A]
time = 1.23, size = 10, normalized size = 0.83 \begin {gather*} \frac {2 \, \sqrt {b x}}{b} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(b*x)^(1/2),x, algorithm="giac")

[Out]

2*sqrt(b*x)/b

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Mupad [B]
time = 0.01, size = 10, normalized size = 0.83 \begin {gather*} \frac {2\,\sqrt {b\,x}}{b} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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