Optimal. Leaf size=28 \[ \frac{a \sqrt{c x^2} \log (x)}{x}+b \sqrt{c x^2} \]
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Rubi [A] time = 0.0156603, antiderivative size = 28, 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 \[ \frac{a \sqrt{c x^2} \log (x)}{x}+b \sqrt{c x^2} \]
Antiderivative was successfully verified.
[In] Int[(Sqrt[c*x^2]*(a + b*x))/x^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a \sqrt{c x^{2}} \log{\left (x \right )}}{x} + \frac{\sqrt{c x^{2}} \int b\, dx}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(c*x**2)**(1/2)/x**2,x)
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Mathematica [A] time = 0.00687355, size = 20, normalized size = 0.71 \[ \frac{c x (a \log (x)+b x)}{\sqrt{c x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[(Sqrt[c*x^2]*(a + b*x))/x^2,x]
[Out]
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Maple [A] time = 0.02, size = 20, normalized size = 0.7 \[{\frac{bx+a\ln \left ( x \right ) }{x}\sqrt{c{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(c*x^2)^(1/2)/x^2,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)*(b*x + a)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212534, size = 26, normalized size = 0.93 \[ \frac{\sqrt{c x^{2}}{\left (b x + a \log \left (x\right )\right )}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)*(b*x + a)/x^2,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{c x^{2}} \left (a + b x\right )}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(c*x**2)**(1/2)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.20913, size = 23, normalized size = 0.82 \[{\left (b x{\rm sign}\left (x\right ) + a{\rm ln}\left ({\left | x \right |}\right ){\rm sign}\left (x\right )\right )} \sqrt{c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)*(b*x + a)/x^2,x, algorithm="giac")
[Out]