\(\int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx\) [949]

Optimal result

Integrand size = 15, antiderivative size = 19 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=\frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7} \]

[Out]

3/2*x^(2/3)-6/7*x^(7/6)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14} \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=\frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7} \]

[In]

Int[(1 - Sqrt[x])/x^(1/3),x]

[Out]

(3*x^(2/3))/2 - (6*x^(7/6))/7

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1}{\sqrt [3]{x}}-\sqrt [6]{x}\right ) \, dx \\ & = \frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=\frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7} \]

[In]

Integrate[(1 - Sqrt[x])/x^(1/3),x]

[Out]

(3*x^(2/3))/2 - (6*x^(7/6))/7

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63

method	result	size
derivativedivides	\(\frac {3 x^{\frac {2}{3}}}{2}-\frac {6 x^{\frac {7}{6}}}{7}\)	\(12\)
default	\(\frac {3 x^{\frac {2}{3}}}{2}-\frac {6 x^{\frac {7}{6}}}{7}\)	\(12\)

[In]

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

[Out]

3/2*x^(2/3)-6/7*x^(7/6)

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=-\frac {6}{7} \, x^{\frac {7}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} \]

[In]

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

[Out]

-6/7*x^(7/6) + 3/2*x^(2/3)

Sympy [A] (verification not implemented)

Time = 0.38 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=- \frac {6 x^{\frac {7}{6}}}{7} + \frac {3 x^{\frac {2}{3}}}{2} \]

[In]

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

[Out]

-6*x**(7/6)/7 + 3*x**(2/3)/2

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=-\frac {6}{7} \, x^{\frac {7}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} \]

[In]

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

[Out]

-6/7*x^(7/6) + 3/2*x^(2/3)

Giac [A] (verification not implemented)

none

Time = 0.32 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=-\frac {6}{7} \, x^{\frac {7}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} \]

[In]

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

[Out]

-6/7*x^(7/6) + 3/2*x^(2/3)

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=-\frac {3\,x^{2/3}\,\left (4\,\sqrt {x}-7\right )}{14} \]

[In]

int(-(x^(1/2) - 1)/x^(1/3),x)

[Out]

-(3*x^(2/3)*(4*x^(1/2) - 7))/14