Optimal. Leaf size=77 \[ \frac{80 x^{7/2}}{567}+\frac{400 x^{5/2}}{6561}+\frac{50000 x^{3/2}}{1594323}+\frac{2 x^4}{9}+\frac{200 x^3}{2187}+\frac{2500 x^2}{59049}+\frac{125000 x}{4782969}-\frac{56145628 \sqrt{x}}{43046721}-\frac{280728140 \log \left (5-9 \sqrt{x}\right )}{387420489} \]
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Rubi [A] time = 0.115842, antiderivative size = 77, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 4, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.19 \[ \frac{80 x^{7/2}}{567}+\frac{400 x^{5/2}}{6561}+\frac{50000 x^{3/2}}{1594323}+\frac{2 x^4}{9}+\frac{200 x^3}{2187}+\frac{2500 x^2}{59049}+\frac{125000 x}{4782969}-\frac{56145628 \sqrt{x}}{43046721}-\frac{280728140 \log \left (5-9 \sqrt{x}\right )}{387420489} \]
Antiderivative was successfully verified.
[In] Int[(6 - 8*x^(7/2))/(5 - 9*Sqrt[x]),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{80 x^{\frac{7}{2}}}{567} + \frac{400 x^{\frac{5}{2}}}{6561} + \frac{50000 x^{\frac{3}{2}}}{1594323} + \frac{2 x^{4}}{9} + \frac{200 x^{3}}{2187} + \frac{2500 x^{2}}{59049} - \frac{280728140 \log{\left (- 9 \sqrt{x} + 5 \right )}}{387420489} + 16 \int ^{\sqrt{x}} \frac{78125}{43046721}\, dx - 12 \int ^{\sqrt{x}} \frac{1}{9}\, dx + \frac{250000 \int ^{\sqrt{x}} x\, dx}{4782969} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((6-8*x**(7/2))/(5-9*x**(1/2)),x)
[Out]
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Mathematica [A] time = 0.0322572, size = 66, normalized size = 0.86 \[ \frac{2 \left (9 \left (21257640 x^{7/2}+9185400 x^{5/2}+4725000 x^{3/2}+33480783 x^4+13778100 x^3+6378750 x^2+3937500 x-196509698 \sqrt{x}\right )-982548490 \log \left (5-9 \sqrt{x}\right )\right )}{2711943423} \]
Antiderivative was successfully verified.
[In] Integrate[(6 - 8*x^(7/2))/(5 - 9*Sqrt[x]),x]
[Out]
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Maple [A] time = 0.006, size = 50, normalized size = 0.7 \[{\frac{2\,{x}^{4}}{9}}+{\frac{80}{567}{x}^{{\frac{7}{2}}}}+{\frac{200\,{x}^{3}}{2187}}+{\frac{400}{6561}{x}^{{\frac{5}{2}}}}+{\frac{2500\,{x}^{2}}{59049}}+{\frac{50000}{1594323}{x}^{{\frac{3}{2}}}}+{\frac{125000\,x}{4782969}}-{\frac{56145628}{43046721}\sqrt{x}}-{\frac{280728140}{387420489}\ln \left ( -5+9\,\sqrt{x} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((6-8*x^(7/2))/(5-9*x^(1/2)),x)
[Out]
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Maxima [A] time = 0.722884, size = 66, normalized size = 0.86 \[ \frac{2}{9} \, x^{4} + \frac{80}{567} \, x^{\frac{7}{2}} + \frac{200}{2187} \, x^{3} + \frac{400}{6561} \, x^{\frac{5}{2}} + \frac{2500}{59049} \, x^{2} + \frac{50000}{1594323} \, x^{\frac{3}{2}} + \frac{125000}{4782969} \, x - \frac{56145628}{43046721} \, \sqrt{x} - \frac{280728140}{387420489} \, \log \left (9 \, \sqrt{x} - 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(2*(4*x^(7/2) - 3)/(9*sqrt(x) - 5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265334, size = 66, normalized size = 0.86 \[ \frac{2}{9} \, x^{4} + \frac{200}{2187} \, x^{3} + \frac{2500}{59049} \, x^{2} + \frac{4}{301327047} \,{\left (10628820 \, x^{3} + 4592700 \, x^{2} + 2362500 \, x - 98254849\right )} \sqrt{x} + \frac{125000}{4782969} \, x - \frac{280728140}{387420489} \, \log \left (9 \, \sqrt{x} - 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(2*(4*x^(7/2) - 3)/(9*sqrt(x) - 5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 10.3873, size = 71, normalized size = 0.92 \[ \frac{80 x^{\frac{7}{2}}}{567} + \frac{400 x^{\frac{5}{2}}}{6561} + \frac{50000 x^{\frac{3}{2}}}{1594323} - \frac{56145628 \sqrt{x}}{43046721} + \frac{2 x^{4}}{9} + \frac{200 x^{3}}{2187} + \frac{2500 x^{2}}{59049} + \frac{125000 x}{4782969} - \frac{280728140 \log{\left (\sqrt{x} - \frac{5}{9} \right )}}{387420489} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((6-8*x**(7/2))/(5-9*x**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.266366, size = 68, normalized size = 0.88 \[ \frac{2}{9} \, x^{4} + \frac{80}{567} \, x^{\frac{7}{2}} + \frac{200}{2187} \, x^{3} + \frac{400}{6561} \, x^{\frac{5}{2}} + \frac{2500}{59049} \, x^{2} + \frac{50000}{1594323} \, x^{\frac{3}{2}} + \frac{125000}{4782969} \, x - \frac{56145628}{43046721} \, \sqrt{x} - \frac{280728140}{387420489} \,{\rm ln}\left ({\left | 9 \, \sqrt{x} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(2*(4*x^(7/2) - 3)/(9*sqrt(x) - 5),x, algorithm="giac")
[Out]