\(\int (x^{5/6}-x^3) \, dx\) [1910]

Optimal result

Integrand size = 11, antiderivative size = 17 \[ \int \left (x^{5/6}-x^3\right ) \, dx=\frac {6 x^{11/6}}{11}-\frac {x^4}{4} \]

[Out]

6/11*x^(11/6)-1/4*x^4

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (x^{5/6}-x^3\right ) \, dx=\frac {6 x^{11/6}}{11}-\frac {x^4}{4} \]

[In]

Int[x^(5/6) - x^3,x]

[Out]

(6*x^(11/6))/11 - x^4/4

Rubi steps \begin{align*} \text {integral}& = \frac {6 x^{11/6}}{11}-\frac {x^4}{4} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \left (x^{5/6}-x^3\right ) \, dx=\frac {6 x^{11/6}}{11}-\frac {x^4}{4} \]

[In]

Integrate[x^(5/6) - x^3,x]

[Out]

(6*x^(11/6))/11 - x^4/4

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.71

method	result	size
derivativedivides	\(\frac {6 x^{\frac {11}{6}}}{11}-\frac {x^{4}}{4}\)	\(12\)
default	\(\frac {6 x^{\frac {11}{6}}}{11}-\frac {x^{4}}{4}\)	\(12\)
risch	\(\frac {6 x^{\frac {11}{6}}}{11}-\frac {x^{4}}{4}\)	\(12\)
parts	\(\frac {6 x^{\frac {11}{6}}}{11}-\frac {x^{4}}{4}\)	\(12\)
trager	\(-\frac {\left (x^{3}+x^{2}+x +1\right ) \left (-1+x \right )}{4}+\frac {6 x^{\frac {11}{6}}}{11}\)	\(21\)

[In]

int(x^(5/6)-x^3,x,method=_RETURNVERBOSE)

[Out]

6/11*x^(11/6)-1/4*x^4

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.65 \[ \int \left (x^{5/6}-x^3\right ) \, dx=-\frac {1}{4} \, x^{4} + \frac {6}{11} \, x^{\frac {11}{6}} \]

[In]

integrate(x^(5/6)-x^3,x, algorithm="fricas")

[Out]

-1/4*x^4 + 6/11*x^(11/6)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.71 \[ \int \left (x^{5/6}-x^3\right ) \, dx=\frac {6 x^{\frac {11}{6}}}{11} - \frac {x^{4}}{4} \]

[In]

integrate(x**(5/6)-x**3,x)

[Out]

6*x**(11/6)/11 - x**4/4

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.65 \[ \int \left (x^{5/6}-x^3\right ) \, dx=-\frac {1}{4} \, x^{4} + \frac {6}{11} \, x^{\frac {11}{6}} \]

[In]

integrate(x^(5/6)-x^3,x, algorithm="maxima")

[Out]

-1/4*x^4 + 6/11*x^(11/6)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.65 \[ \int \left (x^{5/6}-x^3\right ) \, dx=-\frac {1}{4} \, x^{4} + \frac {6}{11} \, x^{\frac {11}{6}} \]

[In]

integrate(x^(5/6)-x^3,x, algorithm="giac")

[Out]

-1/4*x^4 + 6/11*x^(11/6)

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.65 \[ \int \left (x^{5/6}-x^3\right ) \, dx=\frac {6\,x^{11/6}}{11}-\frac {x^4}{4} \]

[In]

int(x^(5/6) - x^3,x)

[Out]

(6*x^(11/6))/11 - x^4/4