\(\int \frac {1}{x^{2/3}} \, dx\) [31]

Optimal result

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

[Out]

3*x^(1/3)

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

[In]

Int[x^(-2/3),x]

[Out]

3*x^(1/3)

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}& = 3 \sqrt [3]{x} \\ \end{align*}

Mathematica [A] (verified)

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

[In]

Integrate[x^(-2/3),x]

[Out]

3*x^(1/3)

Maple [A] (verified)

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

method	result	size
gosper	\(3 x^{\frac {1}{3}}\)	\(6\)
derivativedivides	\(3 x^{\frac {1}{3}}\)	\(6\)
default	\(3 x^{\frac {1}{3}}\)	\(6\)
trager	\(3 x^{\frac {1}{3}}\)	\(6\)
risch	\(3 x^{\frac {1}{3}}\)	\(6\)

[In]

int(1/x^(2/3),x,method=_RETURNVERBOSE)

[Out]

3*x^(1/3)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{x^{2/3}} \, dx=3 \, x^{\frac {1}{3}} \]

[In]

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

[Out]

3*x^(1/3)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{x^{2/3}} \, dx=3 \sqrt [3]{x} \]

[In]

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

[Out]

3*x**(1/3)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{x^{2/3}} \, dx=3 \, x^{\frac {1}{3}} \]

[In]

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

[Out]

3*x^(1/3)

Giac [A] (verification not implemented)

none

Time = 0.38 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{x^{2/3}} \, dx=3 \, x^{\frac {1}{3}} \]

[In]

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

[Out]

3*x^(1/3)

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{x^{2/3}} \, dx=3\,x^{1/3} \]

[In]

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

[Out]

3*x^(1/3)