\(\int x^{5/3} \, dx\) [26]

Optimal result

Integrand size = 5, antiderivative size = 9 \[ \int x^{5/3} \, dx=\frac {3 x^{8/3}}{8} \]

[Out]

3/8*x^(8/3)

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} \[ \int x^{5/3} \, dx=\frac {3 x^{8/3}}{8} \]

[In]

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

[Out]

(3*x^(8/3))/8

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 x^{8/3}}{8} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int x^{5/3} \, dx=\frac {3 x^{8/3}}{8} \]

[In]

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

[Out]

(3*x^(8/3))/8

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67

method	result	size
gosper	\(\frac {3 x^{\frac {8}{3}}}{8}\)	\(6\)
derivativedivides	\(\frac {3 x^{\frac {8}{3}}}{8}\)	\(6\)
default	\(\frac {3 x^{\frac {8}{3}}}{8}\)	\(6\)
trager	\(\frac {3 x^{\frac {8}{3}}}{8}\)	\(6\)
risch	\(\frac {3 x^{\frac {8}{3}}}{8}\)	\(6\)

[In]

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

[Out]

3/8*x^(8/3)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int x^{5/3} \, dx=\frac {3}{8} \, x^{\frac {8}{3}} \]

[In]

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

[Out]

3/8*x^(8/3)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int x^{5/3} \, dx=\frac {3 x^{\frac {8}{3}}}{8} \]

[In]

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

[Out]

3*x**(8/3)/8

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int x^{5/3} \, dx=\frac {3}{8} \, x^{\frac {8}{3}} \]

[In]

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

[Out]

3/8*x^(8/3)

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int x^{5/3} \, dx=\frac {3}{8} \, x^{\frac {8}{3}} \]

[In]

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

[Out]

3/8*x^(8/3)

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int x^{5/3} \, dx=\frac {3\,x^{8/3}}{8} \]

[In]

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

[Out]

(3*x^(8/3))/8