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

Optimal result

Integrand size = 7, antiderivative size = 12 \[ \int \frac {1}{\sqrt {b x}} \, dx=\frac {2 \sqrt {b x}}{b} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32} \[ \int \frac {1}{\sqrt {b x}} \, dx=\frac {2 \sqrt {b x}}{b} \]

[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*} \text {integral}& = \frac {2 \sqrt {b x}}{b} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{\sqrt {b x}} \, dx=\frac {2 x}{\sqrt {b x}} \]

[In]

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

[Out]

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

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75

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	\(\frac {2 \sqrt {b x}}{b}\)	\(11\)
pseudoelliptic	\(\frac {2 \sqrt {b x}}{b}\)	\(11\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{\sqrt {b x}} \, dx=\frac {2 \, \sqrt {b x}}{b} \]

[In]

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

[Out]

2*sqrt(b*x)/b

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {1}{\sqrt {b x}} \, dx=\frac {2 \sqrt {b x}}{b} \]

[In]

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

[Out]

2*sqrt(b*x)/b

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{\sqrt {b x}} \, dx=\frac {2 \, \sqrt {b x}}{b} \]

[In]

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

[Out]

2*sqrt(b*x)/b

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{\sqrt {b x}} \, dx=\frac {2 \, \sqrt {b x}}{b} \]

[In]

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

[Out]

2*sqrt(b*x)/b

Mupad [B] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{\sqrt {b x}} \, dx=\frac {2\,\sqrt {b\,x}}{b} \]

[In]

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

[Out]

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