Optimal. Leaf size=60 \[ \frac{8 a^4}{b (a-b x)^2}-\frac{32 a^3}{b (a-b x)}-\frac{24 a^2 \log (a-b x)}{b}-7 a x-\frac{b x^2}{2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.106563, antiderivative size = 60, 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 \[ \frac{8 a^4}{b (a-b x)^2}-\frac{32 a^3}{b (a-b x)}-\frac{24 a^2 \log (a-b x)}{b}-7 a x-\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^7/(a^2 - b^2*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{8 a^{4}}{b \left (a - b x\right )^{2}} - \frac{32 a^{3}}{b \left (a - b x\right )} - \frac{24 a^{2} \log{\left (a - b x \right )}}{b} - 7 a x - b \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**7/(-b**2*x**2+a**2)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0583979, size = 62, normalized size = 1.03 \[ \frac{8 a^4}{b (b x-a)^2}+\frac{32 a^3}{b (b x-a)}-\frac{24 a^2 \log (a-b x)}{b}-7 a x-\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^7/(a^2 - b^2*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 62, normalized size = 1. \[ -{\frac{b{x}^{2}}{2}}-7\,ax-24\,{\frac{{a}^{2}\ln \left ( bx-a \right ) }{b}}+32\,{\frac{{a}^{3}}{b \left ( bx-a \right ) }}+8\,{\frac{{a}^{4}}{b \left ( bx-a \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^7/(-b^2*x^2+a^2)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.689129, size = 86, normalized size = 1.43 \[ -\frac{1}{2} \, b x^{2} - 7 \, a x - \frac{24 \, a^{2} \log \left (b x - a\right )}{b} + \frac{8 \,{\left (4 \, a^{3} b x - 3 \, a^{4}\right )}}{b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^7/(b^2*x^2 - a^2)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.208773, size = 128, normalized size = 2.13 \[ -\frac{b^{4} x^{4} + 12 \, a b^{3} x^{3} - 27 \, a^{2} b^{2} x^{2} - 50 \, a^{3} b x + 48 \, a^{4} + 48 \,{\left (a^{2} b^{2} x^{2} - 2 \, a^{3} b x + a^{4}\right )} \log \left (b x - a\right )}{2 \,{\left (b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^7/(b^2*x^2 - a^2)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.87014, size = 58, normalized size = 0.97 \[ - \frac{24 a^{2} \log{\left (- a + b x \right )}}{b} - 7 a x - \frac{b x^{2}}{2} + \frac{- 24 a^{4} + 32 a^{3} b x}{a^{2} b - 2 a b^{2} x + b^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**7/(-b**2*x**2+a**2)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.218841, size = 88, normalized size = 1.47 \[ -\frac{24 \, a^{2}{\rm ln}\left ({\left | b x - a \right |}\right )}{b} + \frac{8 \,{\left (4 \, a^{3} b x - 3 \, a^{4}\right )}}{{\left (b x - a\right )}^{2} b} - \frac{b^{7} x^{2} + 14 \, a b^{6} x}{2 \, b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^7/(b^2*x^2 - a^2)^3,x, algorithm="giac")
[Out]