Optimal. Leaf size=32 \[ -\frac{a^2}{3 x^3}-\frac{4 a b}{5 x^{5/2}}-\frac{b^2}{2 x^2} \]
[Out]
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Rubi [A] time = 0.0433862, antiderivative size = 32, 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 \[ -\frac{a^2}{3 x^3}-\frac{4 a b}{5 x^{5/2}}-\frac{b^2}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^2/x^4,x]
[Out]
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Rubi in Sympy [A] time = 6.48894, size = 29, normalized size = 0.91 \[ - \frac{a^{2}}{3 x^{3}} - \frac{4 a b}{5 x^{\frac{5}{2}}} - \frac{b^{2}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**2/x**4,x)
[Out]
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Mathematica [A] time = 0.0129686, size = 28, normalized size = 0.88 \[ -\frac{10 a^2+24 a b \sqrt{x}+15 b^2 x}{30 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^2/x^4,x]
[Out]
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Maple [A] time = 0.001, size = 25, normalized size = 0.8 \[ -{\frac{{a}^{2}}{3\,{x}^{3}}}-{\frac{4\,ab}{5}{x}^{-{\frac{5}{2}}}}-{\frac{{b}^{2}}{2\,{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^2/x^4,x)
[Out]
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Maxima [A] time = 1.42593, size = 32, normalized size = 1. \[ -\frac{15 \, b^{2} x + 24 \, a b \sqrt{x} + 10 \, a^{2}}{30 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233807, size = 32, normalized size = 1. \[ -\frac{15 \, b^{2} x + 24 \, a b \sqrt{x} + 10 \, a^{2}}{30 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.24662, size = 29, normalized size = 0.91 \[ - \frac{a^{2}}{3 x^{3}} - \frac{4 a b}{5 x^{\frac{5}{2}}} - \frac{b^{2}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**2/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.218457, size = 32, normalized size = 1. \[ -\frac{15 \, b^{2} x + 24 \, a b \sqrt{x} + 10 \, a^{2}}{30 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^4,x, algorithm="giac")
[Out]