Optimal. Leaf size=42 \[ -\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}-\frac{b}{a^2 (a+b x)}-\frac{1}{a^2 x} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0577944, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}-\frac{b}{a^2 (a+b x)}-\frac{1}{a^2 x} \]
Antiderivative was successfully verified.
[In] Int[x^2/(a*x^2 + b*x^3)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.1573, size = 39, normalized size = 0.93 \[ - \frac{b}{a^{2} \left (a + b x\right )} - \frac{1}{a^{2} x} - \frac{2 b \log{\left (x \right )}}{a^{3}} + \frac{2 b \log{\left (a + b x \right )}}{a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(b*x**3+a*x**2)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0703691, size = 35, normalized size = 0.83 \[ -\frac{a \left (\frac{b}{a+b x}+\frac{1}{x}\right )-2 b \log (a+b x)+2 b \log (x)}{a^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(a*x^2 + b*x^3)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.017, size = 43, normalized size = 1. \[ -{\frac{1}{{a}^{2}x}}-{\frac{b}{{a}^{2} \left ( bx+a \right ) }}-2\,{\frac{b\ln \left ( x \right ) }{{a}^{3}}}+2\,{\frac{b\ln \left ( bx+a \right ) }{{a}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(b*x^3+a*x^2)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 7.04686, size = 61, normalized size = 1.45 \[ -\frac{2 \, b x + a}{a^{2} b x^{2} + a^{3} x} + \frac{2 \, b \log \left (b x + a\right )}{a^{3}} - \frac{2 \, b \log \left (x\right )}{a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^3 + a*x^2)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.216112, size = 85, normalized size = 2.02 \[ -\frac{2 \, a b x + a^{2} - 2 \,{\left (b^{2} x^{2} + a b x\right )} \log \left (b x + a\right ) + 2 \,{\left (b^{2} x^{2} + a b x\right )} \log \left (x\right )}{a^{3} b x^{2} + a^{4} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^3 + a*x^2)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.57812, size = 36, normalized size = 0.86 \[ - \frac{a + 2 b x}{a^{3} x + a^{2} b x^{2}} + \frac{2 b \left (- \log{\left (x \right )} + \log{\left (\frac{a}{b} + x \right )}\right )}{a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(b*x**3+a*x**2)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.219218, size = 61, normalized size = 1.45 \[ \frac{2 \, b{\rm ln}\left ({\left | b x + a \right |}\right )}{a^{3}} - \frac{2 \, b{\rm ln}\left ({\left | x \right |}\right )}{a^{3}} - \frac{2 \, b x + a}{{\left (b x^{2} + a x\right )} a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^3 + a*x^2)^2,x, algorithm="giac")
[Out]