\(\int (a+\frac {b}{\sqrt [3]{x}}) \, dx\) [2398]

Optimal result

Integrand size = 9, antiderivative size = 14 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=\frac {3}{2} b x^{2/3}+a x \]

[Out]

3/2*b*x^(2/3)+a*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, 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 = {} \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a x+\frac {3}{2} b x^{2/3} \]

[In]

Int[a + b/x^(1/3),x]

[Out]

(3*b*x^(2/3))/2 + a*x

Rubi steps \begin{align*} \text {integral}& = \frac {3}{2} b x^{2/3}+a x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=\frac {3}{2} b x^{2/3}+a x \]

[In]

Integrate[a + b/x^(1/3),x]

[Out]

(3*b*x^(2/3))/2 + a*x

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79

method	result	size
derivativedivides	\(\frac {3 b \,x^{\frac {2}{3}}}{2}+a x\)	\(11\)
default	\(\frac {3 b \,x^{\frac {2}{3}}}{2}+a x\)	\(11\)
risch	\(\frac {3 b \,x^{\frac {2}{3}}}{2}+a x\)	\(11\)
trager	\(a \left (-1+x \right )+\frac {3 b \,x^{\frac {2}{3}}}{2}\)	\(13\)

[In]

int(a+b/x^(1/3),x,method=_RETURNVERBOSE)

[Out]

3/2*b*x^(2/3)+a*x

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a x + \frac {3}{2} \, b x^{\frac {2}{3}} \]

[In]

integrate(a+b/x^(1/3),x, algorithm="fricas")

[Out]

a*x + 3/2*b*x^(2/3)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a x + \frac {3 b x^{\frac {2}{3}}}{2} \]

[In]

integrate(a+b/x**(1/3),x)

[Out]

a*x + 3*b*x**(2/3)/2

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a x + \frac {3}{2} \, b x^{\frac {2}{3}} \]

[In]

integrate(a+b/x^(1/3),x, algorithm="maxima")

[Out]

a*x + 3/2*b*x^(2/3)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a x + \frac {3}{2} \, b x^{\frac {2}{3}} \]

[In]

integrate(a+b/x^(1/3),x, algorithm="giac")

[Out]

a*x + 3/2*b*x^(2/3)

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a\,x+\frac {3\,b\,x^{2/3}}{2} \]

[In]

int(a + b/x^(1/3),x)

[Out]

a*x + (3*b*x^(2/3))/2