Optimal. Leaf size=41 \[ -\frac{a}{6 c^2 x^5 \sqrt{c x^2}}-\frac{b}{5 c^2 x^4 \sqrt{c x^2}} \]
[Out]
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Rubi [A] time = 0.0232365, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{a}{6 c^2 x^5 \sqrt{c x^2}}-\frac{b}{5 c^2 x^4 \sqrt{c x^2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/(x^2*(c*x^2)^(5/2)),x]
[Out]
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Rubi in Sympy [A] time = 9.21953, size = 37, normalized size = 0.9 \[ - \frac{a \sqrt{c x^{2}}}{6 c^{3} x^{7}} - \frac{b \sqrt{c x^{2}}}{5 c^{3} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/x**2/(c*x**2)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0124851, size = 27, normalized size = 0.66 \[ -\frac{\sqrt{c x^2} (5 a+6 b x)}{30 c^3 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/(x^2*(c*x^2)^(5/2)),x]
[Out]
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Maple [A] time = 0.004, size = 21, normalized size = 0.5 \[ -{\frac{6\,bx+5\,a}{30\,x} \left ( c{x}^{2} \right ) ^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/x^2/(c*x^2)^(5/2),x)
[Out]
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Maxima [A] time = 1.31975, size = 26, normalized size = 0.63 \[ -\frac{b}{5 \, c^{\frac{5}{2}} x^{5}} - \frac{a}{6 \, c^{\frac{5}{2}} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/((c*x^2)^(5/2)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209571, size = 31, normalized size = 0.76 \[ -\frac{\sqrt{c x^{2}}{\left (6 \, b x + 5 \, a\right )}}{30 \, c^{3} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/((c*x^2)^(5/2)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.10562, size = 32, normalized size = 0.78 \[ - \frac{a}{6 c^{\frac{5}{2}} x \left (x^{2}\right )^{\frac{5}{2}}} - \frac{b}{5 c^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/x**2/(c*x**2)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.535343, size = 4, normalized size = 0.1 \[ \mathit{sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/((c*x^2)^(5/2)*x^2),x, algorithm="giac")
[Out]