\(\int \frac {1}{x^{5/3}} \, dx\) [33]

Optimal result

Integrand size = 5, antiderivative size = 9 \[ \int \frac {1}{x^{5/3}} \, dx=-\frac {3}{2 x^{2/3}} \]

[Out]

-3/2/x^(2/3)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, 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} \[ \int \frac {1}{x^{5/3}} \, dx=-\frac {3}{2 x^{2/3}} \]

[In]

Int[x^(-5/3),x]

[Out]

-3/(2*x^(2/3))

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 {3}{2 x^{2/3}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^{5/3}} \, dx=-\frac {3}{2 x^{2/3}} \]

[In]

Integrate[x^(-5/3),x]

[Out]

-3/(2*x^(2/3))

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67

method	result	size
gosper	\(-\frac {3}{2 x^{\frac {2}{3}}}\)	\(6\)
derivativedivides	\(-\frac {3}{2 x^{\frac {2}{3}}}\)	\(6\)
default	\(-\frac {3}{2 x^{\frac {2}{3}}}\)	\(6\)
trager	\(-\frac {3}{2 x^{\frac {2}{3}}}\)	\(6\)
risch	\(-\frac {3}{2 x^{\frac {2}{3}}}\)	\(6\)

[In]

int(1/x^(5/3),x,method=_RETURNVERBOSE)

[Out]

-3/2/x^(2/3)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \frac {1}{x^{5/3}} \, dx=-\frac {3}{2 \, x^{\frac {2}{3}}} \]

[In]

integrate(1/x^(5/3),x, algorithm="fricas")

[Out]

-3/2/x^(2/3)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int \frac {1}{x^{5/3}} \, dx=- \frac {3}{2 x^{\frac {2}{3}}} \]

[In]

integrate(1/x**(5/3),x)

[Out]

-3/(2*x**(2/3))

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \frac {1}{x^{5/3}} \, dx=-\frac {3}{2 \, x^{\frac {2}{3}}} \]

[In]

integrate(1/x^(5/3),x, algorithm="maxima")

[Out]

-3/2/x^(2/3)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \frac {1}{x^{5/3}} \, dx=-\frac {3}{2 \, x^{\frac {2}{3}}} \]

[In]

integrate(1/x^(5/3),x, algorithm="giac")

[Out]

-3/2/x^(2/3)

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \frac {1}{x^{5/3}} \, dx=-\frac {3}{2\,x^{2/3}} \]

[In]

int(1/x^(5/3),x)

[Out]

-3/(2*x^(2/3))