Optimal. Leaf size=70 \[ -\frac{5 a^{3/2} \tanh ^{-1}\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right )}{b^{7/2}}+\frac{5 a \sqrt{x}}{b^3}+\frac{x^{5/2}}{b (a-b x)}+\frac{5 x^{3/2}}{3 b^2} \]
[Out]
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Rubi [A] time = 0.0600947, antiderivative size = 70, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.267 \[ -\frac{5 a^{3/2} \tanh ^{-1}\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right )}{b^{7/2}}+\frac{5 a \sqrt{x}}{b^3}+\frac{x^{5/2}}{b (a-b x)}+\frac{5 x^{3/2}}{3 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)/(-a + b*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 12.5414, size = 63, normalized size = 0.9 \[ - \frac{5 a^{\frac{3}{2}} \operatorname{atanh}{\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right )}}{b^{\frac{7}{2}}} + \frac{5 a \sqrt{x}}{b^{3}} + \frac{x^{\frac{5}{2}}}{b \left (a - b x\right )} + \frac{5 x^{\frac{3}{2}}}{3 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)/(b*x-a)**2,x)
[Out]
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Mathematica [A] time = 0.0762452, size = 70, normalized size = 1. \[ \frac{\sqrt{x} \left (-15 a^2+10 a b x+2 b^2 x^2\right )}{3 b^3 (b x-a)}-\frac{5 a^{3/2} \tanh ^{-1}\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right )}{b^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)/(-a + b*x)^2,x]
[Out]
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Maple [A] time = 0.017, size = 61, normalized size = 0.9 \[ 2\,{\frac{{a}^{2}}{{b}^{3}} \left ( -1/2\,{\frac{\sqrt{x}}{bx-a}}-5/2\,{\frac{1}{\sqrt{ab}}{\it Artanh} \left ({\frac{b\sqrt{x}}{\sqrt{ab}}} \right ) } \right ) }+2\,{\frac{1/3\,b{x}^{3/2}+2\,a\sqrt{x}}{{b}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)/(b*x-a)^2,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(5/2)/(b*x - a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220413, size = 1, normalized size = 0.01 \[ \left [\frac{15 \,{\left (a b x - a^{2}\right )} \sqrt{\frac{a}{b}} \log \left (\frac{b x - 2 \, b \sqrt{x} \sqrt{\frac{a}{b}} + a}{b x - a}\right ) + 2 \,{\left (2 \, b^{2} x^{2} + 10 \, a b x - 15 \, a^{2}\right )} \sqrt{x}}{6 \,{\left (b^{4} x - a b^{3}\right )}}, -\frac{15 \,{\left (a b x - a^{2}\right )} \sqrt{-\frac{a}{b}} \arctan \left (\frac{\sqrt{x}}{\sqrt{-\frac{a}{b}}}\right ) -{\left (2 \, b^{2} x^{2} + 10 \, a b x - 15 \, a^{2}\right )} \sqrt{x}}{3 \,{\left (b^{4} x - a b^{3}\right )}}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(5/2)/(b*x - a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 13.4514, size = 1142, normalized size = 16.31 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)/(b*x-a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.206269, size = 93, normalized size = 1.33 \[ \frac{5 \, a^{2} \arctan \left (\frac{b \sqrt{x}}{\sqrt{-a b}}\right )}{\sqrt{-a b} b^{3}} - \frac{a^{2} \sqrt{x}}{{\left (b x - a\right )} b^{3}} + \frac{2 \,{\left (b^{4} x^{\frac{3}{2}} + 6 \, a b^{3} \sqrt{x}\right )}}{3 \, b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(5/2)/(b*x - a)^2,x, algorithm="giac")
[Out]