\(\int \frac {1}{x^{3/2}} \, dx\) [24]

Optimal result

Integrand size = 5, antiderivative size = 7 \[ \int \frac {1}{x^{3/2}} \, dx=-\frac {2}{\sqrt {x}} \]

[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} \[ \int \frac {1}{x^{3/2}} \, dx=-\frac {2}{\sqrt {x}} \]

[In]

Int[x^(-3/2),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}& = -\frac {2}{\sqrt {x}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^{3/2}} \, dx=-\frac {2}{\sqrt {x}} \]

[In]

Integrate[x^(-3/2),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	\(-\frac {2}{\sqrt {x}}\)	\(6\)
derivativedivides	\(-\frac {2}{\sqrt {x}}\)	\(6\)
default	\(-\frac {2}{\sqrt {x}}\)	\(6\)
trager	\(-\frac {2}{\sqrt {x}}\)	\(6\)
risch	\(-\frac {2}{\sqrt {x}}\)	\(6\)

[In]

int(1/x^(3/2),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 \[ \int \frac {1}{x^{3/2}} \, dx=-\frac {2}{\sqrt {x}} \]

[In]

integrate(1/x^(3/2),x, algorithm="fricas")

[Out]

-2/sqrt(x)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^{3/2}} \, dx=- \frac {2}{\sqrt {x}} \]

[In]

integrate(1/x**(3/2),x)

[Out]

-2/sqrt(x)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{x^{3/2}} \, dx=-\frac {2}{\sqrt {x}} \]

[In]

integrate(1/x^(3/2),x, algorithm="maxima")

[Out]

-2/sqrt(x)

Giac [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{x^{3/2}} \, dx=-\frac {2}{\sqrt {x}} \]

[In]

integrate(1/x^(3/2),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 \[ \int \frac {1}{x^{3/2}} \, dx=-\frac {2}{\sqrt {x}} \]

[In]

int(1/x^(3/2),x)

[Out]

-2/x^(1/2)