Optimal. Leaf size=26 \[ -\frac{(a+b x)^2}{2 a x \sqrt{c x^2}} \]
[Out]
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Rubi [A] time = 0.0138498, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{(a+b x)^2}{2 a x \sqrt{c x^2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/(x^2*Sqrt[c*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 9.06509, size = 32, normalized size = 1.23 \[ - \frac{a \sqrt{c x^{2}}}{2 c x^{3}} - \frac{b \sqrt{c x^{2}}}{c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/x**2/(c*x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00900688, size = 23, normalized size = 0.88 \[ \frac{c x (-a-2 b x)}{2 \left (c x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/(x^2*Sqrt[c*x^2]),x]
[Out]
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Maple [A] time = 0.004, size = 19, normalized size = 0.7 \[ -{\frac{2\,bx+a}{2\,x}{\frac{1}{\sqrt{c{x}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/x^2/(c*x^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.34348, size = 26, normalized size = 1. \[ -\frac{b}{\sqrt{c} x} - \frac{a}{2 \, \sqrt{c} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(sqrt(c*x^2)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208279, size = 28, normalized size = 1.08 \[ -\frac{\sqrt{c x^{2}}{\left (2 \, b x + a\right )}}{2 \, c x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(sqrt(c*x^2)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.0305, size = 31, normalized size = 1.19 \[ - \frac{a}{2 \sqrt{c} x \sqrt{x^{2}}} - \frac{b}{\sqrt{c} \sqrt{x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/x**2/(c*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.574227, size = 4, normalized size = 0.15 \[ \mathit{sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(sqrt(c*x^2)*x^2),x, algorithm="giac")
[Out]