Optimal. Leaf size=44 \[ -\frac{a^2 A}{x}+b x (2 a B+A b)+a \log (x) (a B+2 A b)+\frac{1}{2} b^2 B x^2 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0750248, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{a^2 A}{x}+b x (2 a B+A b)+a \log (x) (a B+2 A b)+\frac{1}{2} b^2 B x^2 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^2*(A + B*x))/x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{2}}{x} + B b^{2} \int x\, dx + a \left (2 A b + B a\right ) \log{\left (x \right )} + \frac{b \left (A b + 2 B a\right ) \int A\, dx}{A} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**2*(B*x+A)/x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0380607, size = 43, normalized size = 0.98 \[ -\frac{a^2 A}{x}+a \log (x) (a B+2 A b)+2 a b B x+\frac{1}{2} b^2 x (2 A+B x) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^2*(A + B*x))/x^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 46, normalized size = 1.1 \[{\frac{{b}^{2}B{x}^{2}}{2}}+Ax{b}^{2}+2\,Bxab+2\,A\ln \left ( x \right ) ab+B\ln \left ( x \right ){a}^{2}-{\frac{A{a}^{2}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^2*(B*x+A)/x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34989, size = 62, normalized size = 1.41 \[ \frac{1}{2} \, B b^{2} x^{2} - \frac{A a^{2}}{x} +{\left (2 \, B a b + A b^{2}\right )} x +{\left (B a^{2} + 2 \, A a b\right )} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2/x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.204609, size = 70, normalized size = 1.59 \[ \frac{B b^{2} x^{3} - 2 \, A a^{2} + 2 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 2 \,{\left (B a^{2} + 2 \, A a b\right )} x \log \left (x\right )}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2/x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.42724, size = 42, normalized size = 0.95 \[ - \frac{A a^{2}}{x} + \frac{B b^{2} x^{2}}{2} + a \left (2 A b + B a\right ) \log{\left (x \right )} + x \left (A b^{2} + 2 B a b\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**2*(B*x+A)/x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.270435, size = 62, normalized size = 1.41 \[ \frac{1}{2} \, B b^{2} x^{2} + 2 \, B a b x + A b^{2} x - \frac{A a^{2}}{x} +{\left (B a^{2} + 2 \, A a b\right )}{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2/x^2,x, algorithm="giac")
[Out]