Optimal. Leaf size=29 \[ \frac{a x \log (x)}{\sqrt{c x^2}}+\frac{b x^2}{\sqrt{c x^2}} \]
[Out]
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Rubi [A] time = 0.0149554, antiderivative size = 29, 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 \[ \frac{a x \log (x)}{\sqrt{c x^2}}+\frac{b x^2}{\sqrt{c x^2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/Sqrt[c*x^2],x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a \sqrt{c x^{2}} \log{\left (x \right )}}{c x} + \frac{\sqrt{c x^{2}} \int b\, dx}{c x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/(c*x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00582401, size = 19, normalized size = 0.66 \[ \frac{x (a \log (x)+b x)}{\sqrt{c x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/Sqrt[c*x^2],x]
[Out]
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Maple [A] time = 0.005, size = 18, normalized size = 0.6 \[{x \left ( bx+a\ln \left ( x \right ) \right ){\frac{1}{\sqrt{c{x}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/(c*x^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.33998, size = 27, normalized size = 0.93 \[ \frac{a \log \left (x\right )}{\sqrt{c}} + \frac{\sqrt{c x^{2}} b}{c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/sqrt(c*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214175, size = 30, normalized size = 1.03 \[ \frac{\sqrt{c x^{2}}{\left (b x + a \log \left (x\right )\right )}}{c x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/sqrt(c*x^2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{a + b x}{\sqrt{c x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/(c*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212215, size = 47, normalized size = 1.62 \[ -\frac{a{\rm ln}\left ({\left | -\sqrt{c} x + \sqrt{c x^{2}} \right |}\right )}{\sqrt{c}} + \frac{\sqrt{c x^{2}} b}{c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/sqrt(c*x^2),x, algorithm="giac")
[Out]