Optimal. Leaf size=75 \[ -\frac{a^5}{5 x^5}-\frac{10 a^4 b}{9 x^{9/2}}-\frac{5 a^3 b^2}{2 x^4}-\frac{20 a^2 b^3}{7 x^{7/2}}-\frac{5 a b^4}{3 x^3}-\frac{2 b^5}{5 x^{5/2}} \]
[Out]
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Rubi [A] time = 0.0864623, antiderivative size = 75, 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 \[ -\frac{a^5}{5 x^5}-\frac{10 a^4 b}{9 x^{9/2}}-\frac{5 a^3 b^2}{2 x^4}-\frac{20 a^2 b^3}{7 x^{7/2}}-\frac{5 a b^4}{3 x^3}-\frac{2 b^5}{5 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^5/x^6,x]
[Out]
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Rubi in Sympy [A] time = 13.6197, size = 75, normalized size = 1. \[ - \frac{a^{5}}{5 x^{5}} - \frac{10 a^{4} b}{9 x^{\frac{9}{2}}} - \frac{5 a^{3} b^{2}}{2 x^{4}} - \frac{20 a^{2} b^{3}}{7 x^{\frac{7}{2}}} - \frac{5 a b^{4}}{3 x^{3}} - \frac{2 b^{5}}{5 x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**5/x**6,x)
[Out]
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Mathematica [A] time = 0.0218488, size = 65, normalized size = 0.87 \[ -\frac{126 a^5+700 a^4 b \sqrt{x}+1575 a^3 b^2 x+1800 a^2 b^3 x^{3/2}+1050 a b^4 x^2+252 b^5 x^{5/2}}{630 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^5/x^6,x]
[Out]
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Maple [A] time = 0.004, size = 58, normalized size = 0.8 \[ -{\frac{{a}^{5}}{5\,{x}^{5}}}-{\frac{10\,{a}^{4}b}{9}{x}^{-{\frac{9}{2}}}}-{\frac{5\,{a}^{3}{b}^{2}}{2\,{x}^{4}}}-{\frac{20\,{a}^{2}{b}^{3}}{7}{x}^{-{\frac{7}{2}}}}-{\frac{5\,a{b}^{4}}{3\,{x}^{3}}}-{\frac{2\,{b}^{5}}{5}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^5/x^6,x)
[Out]
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Maxima [A] time = 1.44488, size = 77, normalized size = 1.03 \[ -\frac{252 \, b^{5} x^{\frac{5}{2}} + 1050 \, a b^{4} x^{2} + 1800 \, a^{2} b^{3} x^{\frac{3}{2}} + 1575 \, a^{3} b^{2} x + 700 \, a^{4} b \sqrt{x} + 126 \, a^{5}}{630 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236644, size = 78, normalized size = 1.04 \[ -\frac{1050 \, a b^{4} x^{2} + 1575 \, a^{3} b^{2} x + 126 \, a^{5} + 4 \,{\left (63 \, b^{5} x^{2} + 450 \, a^{2} b^{3} x + 175 \, a^{4} b\right )} \sqrt{x}}{630 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.82712, size = 75, normalized size = 1. \[ - \frac{a^{5}}{5 x^{5}} - \frac{10 a^{4} b}{9 x^{\frac{9}{2}}} - \frac{5 a^{3} b^{2}}{2 x^{4}} - \frac{20 a^{2} b^{3}}{7 x^{\frac{7}{2}}} - \frac{5 a b^{4}}{3 x^{3}} - \frac{2 b^{5}}{5 x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**5/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.215457, size = 77, normalized size = 1.03 \[ -\frac{252 \, b^{5} x^{\frac{5}{2}} + 1050 \, a b^{4} x^{2} + 1800 \, a^{2} b^{3} x^{\frac{3}{2}} + 1575 \, a^{3} b^{2} x + 700 \, a^{4} b \sqrt{x} + 126 \, a^{5}}{630 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5/x^6,x, algorithm="giac")
[Out]