\(\int \frac {1}{\sqrt {x}} \, dx\) [23]

Optimal result

Integrand size = 5, antiderivative size = 7 \[ \int \frac {1}{\sqrt {x}} \, dx=2 \sqrt {x} \]

[Out]

2*x^(1/2)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {30} \[ \int \frac {1}{\sqrt {x}} \, dx=2 \sqrt {x} \]

[In]

Int[1/Sqrt[x],x]

[Out]

2*Sqrt[x]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps \begin{align*} \text {integral}& = 2 \sqrt {x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int \frac {1}{\sqrt {x}} \, dx=2 \sqrt {x} \]

[In]

Integrate[1/Sqrt[x],x]

[Out]

2*Sqrt[x]

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86

method	result	size
gosper	\(2 \sqrt {x}\)	\(6\)
derivativedivides	\(2 \sqrt {x}\)	\(6\)
default	\(2 \sqrt {x}\)	\(6\)
trager	\(2 \sqrt {x}\)	\(6\)
risch	\(2 \sqrt {x}\)	\(6\)

[In]

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

[Out]

2*x^(1/2)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{\sqrt {x}} \, dx=2 \, \sqrt {x} \]

[In]

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

[Out]

2*sqrt(x)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{\sqrt {x}} \, dx=2 \sqrt {x} \]

[In]

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

[Out]

2*sqrt(x)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{\sqrt {x}} \, dx=2 \, \sqrt {x} \]

[In]

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

[Out]

2*sqrt(x)

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{\sqrt {x}} \, dx=2 \, \sqrt {x} \]

[In]

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

[Out]

2*sqrt(x)

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{\sqrt {x}} \, dx=2\,\sqrt {x} \]

[In]

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

[Out]

2*x^(1/2)