Optimal. Leaf size=49 \[ \frac{4 a^3}{b (a-b x)^2}-\frac{12 a^2}{b (a-b x)}-\frac{6 a \log (a-b x)}{b}-x \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0764532, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{4 a^3}{b (a-b x)^2}-\frac{12 a^2}{b (a-b x)}-\frac{6 a \log (a-b x)}{b}-x \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^6/(a^2 - b^2*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 15.6476, size = 37, normalized size = 0.76 \[ \frac{4 a^{3}}{b \left (a - b x\right )^{2}} - \frac{12 a^{2}}{b \left (a - b x\right )} - \frac{6 a \log{\left (a - b x \right )}}{b} - x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**6/(-b**2*x**2+a**2)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0845142, size = 41, normalized size = 0.84 \[ \frac{4 a^2 (3 b x-2 a)}{b (a-b x)^2}-\frac{6 a \log (a-b x)}{b}-x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^6/(a^2 - b^2*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 53, normalized size = 1.1 \[ -x-6\,{\frac{a\ln \left ( bx-a \right ) }{b}}+12\,{\frac{{a}^{2}}{b \left ( bx-a \right ) }}+4\,{\frac{{a}^{3}}{b \left ( bx-a \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^6/(-b^2*x^2+a^2)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.685486, size = 74, normalized size = 1.51 \[ -x - \frac{6 \, a \log \left (b x - a\right )}{b} + \frac{4 \,{\left (3 \, a^{2} b x - 2 \, a^{3}\right )}}{b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^6/(b^2*x^2 - a^2)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.21379, size = 111, normalized size = 2.27 \[ -\frac{b^{3} x^{3} - 2 \, a b^{2} x^{2} - 11 \, a^{2} b x + 8 \, a^{3} + 6 \,{\left (a b^{2} x^{2} - 2 \, a^{2} b x + a^{3}\right )} \log \left (b x - a\right )}{b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^6/(b^2*x^2 - a^2)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.66382, size = 46, normalized size = 0.94 \[ - \frac{6 a \log{\left (- a + b x \right )}}{b} - x + \frac{- 8 a^{3} + 12 a^{2} b x}{a^{2} b - 2 a b^{2} x + b^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**6/(-b**2*x**2+a**2)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.219657, size = 62, normalized size = 1.27 \[ -x - \frac{6 \, a{\rm ln}\left ({\left | b x - a \right |}\right )}{b} + \frac{4 \,{\left (3 \, a^{2} b x - 2 \, a^{3}\right )}}{{\left (b x - a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^6/(b^2*x^2 - a^2)^3,x, algorithm="giac")
[Out]