Optimal. Leaf size=27 \[ \frac{b x \log (x)}{\sqrt{c x^2}}-\frac{a}{\sqrt{c x^2}} \]
[Out]
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Rubi [A] time = 0.0178087, antiderivative size = 27, 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 \[ \frac{b x \log (x)}{\sqrt{c x^2}}-\frac{a}{\sqrt{c x^2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/(x*Sqrt[c*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 9.06173, size = 31, normalized size = 1.15 \[ - \frac{a \sqrt{c x^{2}}}{c x^{2}} + \frac{b \sqrt{c x^{2}} \log{\left (x \right )}}{c x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/x/(c*x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0102027, size = 23, normalized size = 0.85 \[ \frac{c x^2 (b x \log (x)-a)}{\left (c x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/(x*Sqrt[c*x^2]),x]
[Out]
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Maple [A] time = 0.006, size = 18, normalized size = 0.7 \[{(b\ln \left ( x \right ) x-a){\frac{1}{\sqrt{c{x}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/x/(c*x^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.35178, size = 23, normalized size = 0.85 \[ \frac{b \log \left (x\right )}{\sqrt{c}} - \frac{a}{\sqrt{c} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(sqrt(c*x^2)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221174, size = 31, normalized size = 1.15 \[ \frac{\sqrt{c x^{2}}{\left (b x \log \left (x\right ) - a\right )}}{c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(sqrt(c*x^2)*x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{a + b x}{x \sqrt{c x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/x/(c*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.219873, size = 63, normalized size = 2.33 \[ -\frac{b{\rm ln}\left ({\left | -\sqrt{c} x + \sqrt{c x^{2}} \right |}\right ) - \frac{2 \, a \sqrt{c}}{\sqrt{c} x - \sqrt{c x^{2}}}}{\sqrt{c}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(sqrt(c*x^2)*x),x, algorithm="giac")
[Out]