Optimal. Leaf size=32 \[ \frac{b \sqrt{c x^2} \log (x)}{x}-\frac{a \sqrt{c x^2}}{x^2} \]
[Out]
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Rubi [A] time = 0.019719, antiderivative size = 32, 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 \[ \frac{b \sqrt{c x^2} \log (x)}{x}-\frac{a \sqrt{c x^2}}{x^2} \]
Antiderivative was successfully verified.
[In] Int[(Sqrt[c*x^2]*(a + b*x))/x^3,x]
[Out]
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Rubi in Sympy [A] time = 8.17114, size = 27, normalized size = 0.84 \[ - \frac{a \sqrt{c x^{2}}}{x^{2}} + \frac{b \sqrt{c x^{2}} \log{\left (x \right )}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(c*x**2)**(1/2)/x**3,x)
[Out]
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Mathematica [A] time = 0.00830452, size = 20, normalized size = 0.62 \[ \frac{c (b x \log (x)-a)}{\sqrt{c x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[(Sqrt[c*x^2]*(a + b*x))/x^3,x]
[Out]
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Maple [A] time = 0.006, size = 21, normalized size = 0.7 \[{\frac{b\ln \left ( x \right ) x-a}{{x}^{2}}\sqrt{c{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(c*x^2)^(1/2)/x^3,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^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215828, size = 27, normalized size = 0.84 \[ \frac{\sqrt{c x^{2}}{\left (b x \log \left (x\right ) - a\right )}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)*(b*x + a)/x^3,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{c x^{2}} \left (a + b x\right )}{x^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(c*x**2)**(1/2)/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.207842, size = 27, normalized size = 0.84 \[{\left (b{\rm ln}\left ({\left | x \right |}\right ){\rm sign}\left (x\right ) - \frac{a{\rm sign}\left (x\right )}{x}\right )} \sqrt{c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)*(b*x + a)/x^3,x, algorithm="giac")
[Out]