Optimal. Leaf size=43 \[ -\frac{4 a^2 \log (a-b x)}{b c}-\frac{(a+b x)^2}{2 b c}-\frac{2 a x}{c} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0397019, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ -\frac{4 a^2 \log (a-b x)}{b c}-\frac{(a+b x)^2}{2 b c}-\frac{2 a x}{c} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^2/(a*c - b*c*x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.55382, size = 34, normalized size = 0.79 \[ - \frac{4 a^{2} \log{\left (a - b x \right )}}{b c} - \frac{2 a x}{c} - \frac{\left (a + b x\right )^{2}}{2 b c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**2/(-b*c*x+a*c),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0108964, size = 37, normalized size = 0.86 \[ -\frac{4 a^2 \log (a-b x)}{b c}-\frac{3 a x}{c}-\frac{b x^2}{2 c} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^2/(a*c - b*c*x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 37, normalized size = 0.9 \[ -{\frac{b{x}^{2}}{2\,c}}-3\,{\frac{ax}{c}}-4\,{\frac{{a}^{2}\ln \left ( bx-a \right ) }{bc}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^2/(-b*c*x+a*c),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33979, size = 47, normalized size = 1.09 \[ -\frac{4 \, a^{2} \log \left (b x - a\right )}{b c} - \frac{b x^{2} + 6 \, a x}{2 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^2/(b*c*x - a*c),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.215882, size = 46, normalized size = 1.07 \[ -\frac{b^{2} x^{2} + 6 \, a b x + 8 \, a^{2} \log \left (b x - a\right )}{2 \, b c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^2/(b*c*x - a*c),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.21252, size = 31, normalized size = 0.72 \[ - \frac{4 a^{2} \log{\left (- a + b x \right )}}{b c} - \frac{3 a x}{c} - \frac{b x^{2}}{2 c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**2/(-b*c*x+a*c),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.203873, size = 62, normalized size = 1.44 \[ -\frac{4 \, a^{2}{\rm ln}\left ({\left | b x - a \right |}\right )}{b c} - \frac{b^{3} c x^{2} + 6 \, a b^{2} c x}{2 \, b^{2} c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^2/(b*c*x - a*c),x, algorithm="giac")
[Out]