Optimal. Leaf size=38 \[ \frac{2 \left (a+b \sqrt{x}\right )^5}{5 b^2}-\frac{a \left (a+b \sqrt{x}\right )^4}{2 b^2} \]
[Out]
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Rubi [A] time = 0.0451122, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{2 \left (a+b \sqrt{x}\right )^5}{5 b^2}-\frac{a \left (a+b \sqrt{x}\right )^4}{2 b^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^3,x]
[Out]
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Rubi in Sympy [A] time = 6.77902, size = 32, normalized size = 0.84 \[ - \frac{a \left (a + b \sqrt{x}\right )^{4}}{2 b^{2}} + \frac{2 \left (a + b \sqrt{x}\right )^{5}}{5 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**3,x)
[Out]
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Mathematica [A] time = 0.00854131, size = 40, normalized size = 1.05 \[ a^3 x+2 a^2 b x^{3/2}+\frac{3}{2} a b^2 x^2+\frac{2}{5} b^3 x^{5/2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^3,x]
[Out]
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Maple [A] time = 0.002, size = 33, normalized size = 0.9 \[{\frac{2\,{b}^{3}}{5}{x}^{{\frac{5}{2}}}}+{\frac{3\,a{b}^{2}{x}^{2}}{2}}+2\,{a}^{2}b{x}^{3/2}+{a}^{3}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^3,x)
[Out]
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Maxima [A] time = 1.42096, size = 43, normalized size = 1.13 \[ \frac{2}{5} \, b^{3} x^{\frac{5}{2}} + \frac{3}{2} \, a b^{2} x^{2} + 2 \, a^{2} b x^{\frac{3}{2}} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232683, size = 47, normalized size = 1.24 \[ \frac{3}{2} \, a b^{2} x^{2} + a^{3} x + \frac{2}{5} \,{\left (b^{3} x^{2} + 5 \, a^{2} b x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.21469, size = 39, normalized size = 1.03 \[ a^{3} x + 2 a^{2} b x^{\frac{3}{2}} + \frac{3 a b^{2} x^{2}}{2} + \frac{2 b^{3} x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**3,x)
[Out]
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GIAC/XCAS [A] time = 0.215377, size = 43, normalized size = 1.13 \[ \frac{2}{5} \, b^{3} x^{\frac{5}{2}} + \frac{3}{2} \, a b^{2} x^{2} + 2 \, a^{2} b x^{\frac{3}{2}} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3,x, algorithm="giac")
[Out]