Optimal. Leaf size=61 \[ \frac{1}{5} \left (x^2-10\right )^{5/2}-\frac{10}{3} \left (x^2-10\right )^{3/2}+100 \sqrt{x^2-10}-100 \sqrt{10} \tan ^{-1}\left (\frac{\sqrt{x^2-10}}{\sqrt{10}}\right ) \]
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Rubi [A] time = 0.0689656, antiderivative size = 61, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ \frac{1}{5} \left (x^2-10\right )^{5/2}-\frac{10}{3} \left (x^2-10\right )^{3/2}+100 \sqrt{x^2-10}-100 \sqrt{10} \tan ^{-1}\left (\frac{\sqrt{x^2-10}}{\sqrt{10}}\right ) \]
Antiderivative was successfully verified.
[In] Int[(-10 + x^2)^(5/2)/x,x]
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Rubi in Sympy [A] time = 3.16264, size = 54, normalized size = 0.89 \[ \frac{\left (x^{2} - 10\right )^{\frac{5}{2}}}{5} - \frac{10 \left (x^{2} - 10\right )^{\frac{3}{2}}}{3} + 100 \sqrt{x^{2} - 10} - 100 \sqrt{10} \operatorname{atan}{\left (\frac{\sqrt{10} \sqrt{x^{2} - 10}}{10} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2-10)**(5/2)/x,x)
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Mathematica [A] time = 0.0319282, size = 47, normalized size = 0.77 \[ 100 \sqrt{10} \tan ^{-1}\left (\frac{1}{\sqrt{\frac{x^2}{10}-1}}\right )+\frac{1}{15} \sqrt{x^2-10} \left (3 x^4-110 x^2+2300\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(-10 + x^2)^(5/2)/x,x]
[Out]
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Maple [A] time = 0.009, size = 46, normalized size = 0.8 \[{\frac{1}{5} \left ({x}^{2}-10 \right ) ^{{\frac{5}{2}}}}-{\frac{10}{3} \left ({x}^{2}-10 \right ) ^{{\frac{3}{2}}}}+100\,\sqrt{{x}^{2}-10}+100\,\sqrt{10}\arctan \left ({\frac{\sqrt{10}}{\sqrt{{x}^{2}-10}}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2-10)^(5/2)/x,x)
[Out]
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Maxima [A] time = 1.49045, size = 57, normalized size = 0.93 \[ \frac{1}{5} \,{\left (x^{2} - 10\right )}^{\frac{5}{2}} - \frac{10}{3} \,{\left (x^{2} - 10\right )}^{\frac{3}{2}} + 100 \, \sqrt{10} \arcsin \left (\frac{\sqrt{10}}{{\left | x \right |}}\right ) + 100 \, \sqrt{x^{2} - 10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 10)^(5/2)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210487, size = 217, normalized size = 3.56 \[ -\frac{12 \, x^{10} - 650 \, x^{8} + 17875 \, x^{6} - 197500 \, x^{4} + 775000 \, x^{2} - 3000 \,{\left (\sqrt{10}{\left (4 \, x^{4} - 30 \, x^{2} + 25\right )} \sqrt{x^{2} - 10} - \sqrt{10}{\left (4 \, x^{5} - 50 \, x^{3} + 125 \, x\right )}\right )} \arctan \left (-\frac{1}{10} \, \sqrt{10}{\left (x - \sqrt{x^{2} - 10}\right )}\right ) -{\left (12 \, x^{9} - 590 \, x^{7} + 15075 \, x^{5} - 128750 \, x^{3} + 287500 \, x\right )} \sqrt{x^{2} - 10} - 575000}{15 \,{\left (4 \, x^{5} - 50 \, x^{3} -{\left (4 \, x^{4} - 30 \, x^{2} + 25\right )} \sqrt{x^{2} - 10} + 125 \, x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 10)^(5/2)/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 21.9911, size = 167, normalized size = 2.74 \[ \begin{cases} \frac{x^{4} \sqrt{x^{2} - 10}}{5} - \frac{22 x^{2} \sqrt{x^{2} - 10}}{3} + \frac{460 \sqrt{x^{2} - 10}}{3} - 100 \sqrt{10} i \log{\left (x \right )} + 50 \sqrt{10} i \log{\left (x^{2} \right )} + 100 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{10}}{x} \right )} & \text{for}\: \frac{\left |{x^{2}}\right |}{10} > 1 \\\frac{i x^{4} \sqrt{- x^{2} + 10}}{5} - \frac{22 i x^{2} \sqrt{- x^{2} + 10}}{3} + \frac{460 i \sqrt{- x^{2} + 10}}{3} + 50 \sqrt{10} i \log{\left (x^{2} \right )} - 100 \sqrt{10} i \log{\left (\sqrt{- \frac{x^{2}}{10} + 1} + 1 \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2-10)**(5/2)/x,x)
[Out]
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GIAC/XCAS [A] time = 0.201529, size = 62, normalized size = 1.02 \[ \frac{1}{5} \,{\left (x^{2} - 10\right )}^{\frac{5}{2}} - \frac{10}{3} \,{\left (x^{2} - 10\right )}^{\frac{3}{2}} - 100 \, \sqrt{10} \arctan \left (\frac{1}{10} \, \sqrt{10} \sqrt{x^{2} - 10}\right ) + 100 \, \sqrt{x^{2} - 10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 10)^(5/2)/x,x, algorithm="giac")
[Out]