Optimal. Leaf size=59 \[ -\frac{2 a^2 \left (a+\frac{b}{x}\right )^{3/2}}{3 b^3}-\frac{2 \left (a+\frac{b}{x}\right )^{7/2}}{7 b^3}+\frac{4 a \left (a+\frac{b}{x}\right )^{5/2}}{5 b^3} \]
[Out]
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Rubi [A] time = 0.0779898, antiderivative size = 59, 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 \[ -\frac{2 a^2 \left (a+\frac{b}{x}\right )^{3/2}}{3 b^3}-\frac{2 \left (a+\frac{b}{x}\right )^{7/2}}{7 b^3}+\frac{4 a \left (a+\frac{b}{x}\right )^{5/2}}{5 b^3} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b/x]/x^4,x]
[Out]
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Rubi in Sympy [A] time = 9.79602, size = 49, normalized size = 0.83 \[ - \frac{2 a^{2} \left (a + \frac{b}{x}\right )^{\frac{3}{2}}}{3 b^{3}} + \frac{4 a \left (a + \frac{b}{x}\right )^{\frac{5}{2}}}{5 b^{3}} - \frac{2 \left (a + \frac{b}{x}\right )^{\frac{7}{2}}}{7 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**(1/2)/x**4,x)
[Out]
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Mathematica [A] time = 0.0246777, size = 51, normalized size = 0.86 \[ -\frac{2 \sqrt{a+\frac{b}{x}} \left (8 a^3 x^3-4 a^2 b x^2+3 a b^2 x+15 b^3\right )}{105 b^3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + b/x]/x^4,x]
[Out]
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Maple [A] time = 0.007, size = 44, normalized size = 0.8 \[ -{\frac{ \left ( 2\,ax+2\,b \right ) \left ( 8\,{a}^{2}{x}^{2}-12\,abx+15\,{b}^{2} \right ) }{105\,{b}^{3}{x}^{3}}\sqrt{{\frac{ax+b}{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^(1/2)/x^4,x)
[Out]
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Maxima [A] time = 1.44091, size = 63, normalized size = 1.07 \[ -\frac{2 \,{\left (a + \frac{b}{x}\right )}^{\frac{7}{2}}}{7 \, b^{3}} + \frac{4 \,{\left (a + \frac{b}{x}\right )}^{\frac{5}{2}} a}{5 \, b^{3}} - \frac{2 \,{\left (a + \frac{b}{x}\right )}^{\frac{3}{2}} a^{2}}{3 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225879, size = 66, normalized size = 1.12 \[ -\frac{2 \,{\left (8 \, a^{3} x^{3} - 4 \, a^{2} b x^{2} + 3 \, a b^{2} x + 15 \, b^{3}\right )} \sqrt{\frac{a x + b}{x}}}{105 \, b^{3} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.48161, size = 899, normalized size = 15.24 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**(1/2)/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.256476, size = 197, normalized size = 3.34 \[ \frac{2 \,{\left (140 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{4} a^{2}{\rm sign}\left (x\right ) + 315 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{3} a^{\frac{3}{2}} b{\rm sign}\left (x\right ) + 273 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{2} a b^{2}{\rm sign}\left (x\right ) + 105 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )} \sqrt{a} b^{3}{\rm sign}\left (x\right ) + 15 \, b^{4}{\rm sign}\left (x\right )\right )}}{105 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x)/x^4,x, algorithm="giac")
[Out]