Optimal. Leaf size=70 \[ -\frac{b^2 \left (a+b \sqrt{x}\right )^6}{84 a^3 x^3}+\frac{b \left (a+b \sqrt{x}\right )^6}{14 a^2 x^{7/2}}-\frac{\left (a+b \sqrt{x}\right )^6}{4 a x^4} \]
[Out]
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Rubi [A] time = 0.0757441, antiderivative size = 70, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ -\frac{b^2 \left (a+b \sqrt{x}\right )^6}{84 a^3 x^3}+\frac{b \left (a+b \sqrt{x}\right )^6}{14 a^2 x^{7/2}}-\frac{\left (a+b \sqrt{x}\right )^6}{4 a x^4} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^5/x^5,x]
[Out]
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Rubi in Sympy [A] time = 13.5928, size = 73, normalized size = 1.04 \[ - \frac{a^{5}}{4 x^{4}} - \frac{10 a^{4} b}{7 x^{\frac{7}{2}}} - \frac{10 a^{3} b^{2}}{3 x^{3}} - \frac{4 a^{2} b^{3}}{x^{\frac{5}{2}}} - \frac{5 a b^{4}}{2 x^{2}} - \frac{2 b^{5}}{3 x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**5/x**5,x)
[Out]
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Mathematica [A] time = 0.0218385, size = 65, normalized size = 0.93 \[ -\frac{21 a^5+120 a^4 b \sqrt{x}+280 a^3 b^2 x+336 a^2 b^3 x^{3/2}+210 a b^4 x^2+56 b^5 x^{5/2}}{84 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^5/x^5,x]
[Out]
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Maple [A] time = 0.003, size = 58, normalized size = 0.8 \[ -{\frac{2\,{b}^{5}}{3}{x}^{-{\frac{3}{2}}}}-{\frac{5\,a{b}^{4}}{2\,{x}^{2}}}-4\,{\frac{{a}^{2}{b}^{3}}{{x}^{5/2}}}-{\frac{10\,{a}^{3}{b}^{2}}{3\,{x}^{3}}}-{\frac{10\,{a}^{4}b}{7}{x}^{-{\frac{7}{2}}}}-{\frac{{a}^{5}}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^5/x^5,x)
[Out]
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Maxima [A] time = 1.44165, size = 77, normalized size = 1.1 \[ -\frac{56 \, b^{5} x^{\frac{5}{2}} + 210 \, a b^{4} x^{2} + 336 \, a^{2} b^{3} x^{\frac{3}{2}} + 280 \, a^{3} b^{2} x + 120 \, a^{4} b \sqrt{x} + 21 \, a^{5}}{84 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233861, size = 78, normalized size = 1.11 \[ -\frac{210 \, a b^{4} x^{2} + 280 \, a^{3} b^{2} x + 21 \, a^{5} + 8 \,{\left (7 \, b^{5} x^{2} + 42 \, a^{2} b^{3} x + 15 \, a^{4} b\right )} \sqrt{x}}{84 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.32048, size = 73, normalized size = 1.04 \[ - \frac{a^{5}}{4 x^{4}} - \frac{10 a^{4} b}{7 x^{\frac{7}{2}}} - \frac{10 a^{3} b^{2}}{3 x^{3}} - \frac{4 a^{2} b^{3}}{x^{\frac{5}{2}}} - \frac{5 a b^{4}}{2 x^{2}} - \frac{2 b^{5}}{3 x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**5/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.214445, size = 77, normalized size = 1.1 \[ -\frac{56 \, b^{5} x^{\frac{5}{2}} + 210 \, a b^{4} x^{2} + 336 \, a^{2} b^{3} x^{\frac{3}{2}} + 280 \, a^{3} b^{2} x + 120 \, a^{4} b \sqrt{x} + 21 \, a^{5}}{84 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5/x^5,x, algorithm="giac")
[Out]