Optimal. Leaf size=45 \[ \frac{2}{5} a^3 x^{5/2}+2 a^2 b x^{3/2}+6 a b^2 \sqrt{x}-\frac{2 b^3}{\sqrt{x}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0444258, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{2}{5} a^3 x^{5/2}+2 a^2 b x^{3/2}+6 a b^2 \sqrt{x}-\frac{2 b^3}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3*x^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.92123, size = 44, normalized size = 0.98 \[ \frac{2 a^{3} x^{\frac{5}{2}}}{5} + 2 a^{2} b x^{\frac{3}{2}} + 6 a b^{2} \sqrt{x} - \frac{2 b^{3}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3*x**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0139925, size = 38, normalized size = 0.84 \[ \frac{2 \left (a^3 x^3+5 a^2 b x^2+15 a b^2 x-5 b^3\right )}{5 \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3*x^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 35, normalized size = 0.8 \[{\frac{2\,{a}^{3}{x}^{3}+10\,{a}^{2}b{x}^{2}+30\,a{b}^{2}x-10\,{b}^{3}}{5}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3*x^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.4392, size = 49, normalized size = 1.09 \[ \frac{2}{5} \,{\left (a^{3} + \frac{5 \, a^{2} b}{x} + \frac{15 \, a b^{2}}{x^{2}}\right )} x^{\frac{5}{2}} - \frac{2 \, b^{3}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.228005, size = 46, normalized size = 1.02 \[ \frac{2 \,{\left (a^{3} x^{3} + 5 \, a^{2} b x^{2} + 15 \, a b^{2} x - 5 \, b^{3}\right )}}{5 \, \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 6.69417, size = 44, normalized size = 0.98 \[ \frac{2 a^{3} x^{\frac{5}{2}}}{5} + 2 a^{2} b x^{\frac{3}{2}} + 6 a b^{2} \sqrt{x} - \frac{2 b^{3}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3*x**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.22244, size = 47, normalized size = 1.04 \[ \frac{2}{5} \, a^{3} x^{\frac{5}{2}} + 2 \, a^{2} b x^{\frac{3}{2}} + 6 \, a b^{2} \sqrt{x} - \frac{2 \, b^{3}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^(3/2),x, algorithm="giac")
[Out]