Optimal. Leaf size=40 \[ \frac{4 \left (a+b \sqrt{x}\right )^{3/2}}{3 b^2}-\frac{4 a \sqrt{a+b \sqrt{x}}}{b^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0471729, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{4 \left (a+b \sqrt{x}\right )^{3/2}}{3 b^2}-\frac{4 a \sqrt{a+b \sqrt{x}}}{b^2} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[a + b*Sqrt[x]],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.03321, size = 36, normalized size = 0.9 \[ - \frac{4 a \sqrt{a + b \sqrt{x}}}{b^{2}} + \frac{4 \left (a + b \sqrt{x}\right )^{\frac{3}{2}}}{3 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b*x**(1/2))**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0187558, size = 31, normalized size = 0.78 \[ \frac{4 \left (b \sqrt{x}-2 a\right ) \sqrt{a+b \sqrt{x}}}{3 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[a + b*Sqrt[x]],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 30, normalized size = 0.8 \[ 4\,{\frac{1/3\, \left ( a+b\sqrt{x} \right ) ^{3/2}-a\sqrt{a+b\sqrt{x}}}{{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b*x^(1/2))^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44255, size = 41, normalized size = 1.02 \[ \frac{4 \,{\left (b \sqrt{x} + a\right )}^{\frac{3}{2}}}{3 \, b^{2}} - \frac{4 \, \sqrt{b \sqrt{x} + a} a}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(b*sqrt(x) + a),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.244414, size = 31, normalized size = 0.78 \[ \frac{4 \, \sqrt{b \sqrt{x} + a}{\left (b \sqrt{x} - 2 \, a\right )}}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(b*sqrt(x) + a),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 3.76088, size = 219, normalized size = 5.48 \[ - \frac{8 a^{\frac{7}{2}} x^{2} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{3 a^{2} b^{2} x^{2} + 3 a b^{3} x^{\frac{5}{2}}} + \frac{8 a^{\frac{7}{2}} x^{2}}{3 a^{2} b^{2} x^{2} + 3 a b^{3} x^{\frac{5}{2}}} - \frac{4 a^{\frac{5}{2}} b x^{\frac{5}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{3 a^{2} b^{2} x^{2} + 3 a b^{3} x^{\frac{5}{2}}} + \frac{8 a^{\frac{5}{2}} b x^{\frac{5}{2}}}{3 a^{2} b^{2} x^{2} + 3 a b^{3} x^{\frac{5}{2}}} + \frac{4 a^{\frac{3}{2}} b^{2} x^{3} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{3 a^{2} b^{2} x^{2} + 3 a b^{3} x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b*x**(1/2))**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.258369, size = 36, normalized size = 0.9 \[ \frac{4 \,{\left ({\left (b \sqrt{x} + a\right )}^{\frac{3}{2}} - 3 \, \sqrt{b \sqrt{x} + a} a\right )}}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(b*sqrt(x) + a),x, algorithm="giac")
[Out]