Optimal. Leaf size=26 \[ -\frac{\sqrt{c x^2} (a+b x)^2}{2 a x^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0146623, 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 \[ -\frac{\sqrt{c x^2} (a+b x)^2}{2 a x^3} \]
Antiderivative was successfully verified.
[In] Int[(Sqrt[c*x^2]*(a + b*x))/x^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 8.29241, size = 29, normalized size = 1.12 \[ - \frac{a \sqrt{c x^{2}}}{2 x^{3}} - \frac{b \sqrt{c x^{2}}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(c*x**2)**(1/2)/x**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00663325, size = 22, normalized size = 0.85 \[ -\frac{\sqrt{c x^2} (a+2 b x)}{2 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(Sqrt[c*x^2]*(a + b*x))/x^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 19, normalized size = 0.7 \[ -{\frac{2\,bx+a}{2\,{x}^{3}}\sqrt{c{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(c*x^2)^(1/2)/x^4,x)
[Out]
_______________________________________________________________________________________
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^4,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.207393, size = 24, normalized size = 0.92 \[ -\frac{\sqrt{c x^{2}}{\left (2 \, b x + a\right )}}{2 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)*(b*x + a)/x^4,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.8043, size = 36, normalized size = 1.38 \[ - \frac{a \sqrt{c} \sqrt{x^{2}}}{2 x^{3}} - \frac{b \sqrt{c} \sqrt{x^{2}}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(c*x**2)**(1/2)/x**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.211441, size = 26, normalized size = 1. \[ -\frac{{\left (2 \, b x{\rm sign}\left (x\right ) + a{\rm sign}\left (x\right )\right )} \sqrt{c}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)*(b*x + a)/x^4,x, algorithm="giac")
[Out]