Optimal. Leaf size=104 \[ -\frac{a^5 A}{5 x^5}-\frac{a^4 (a B+5 A b)}{4 x^4}-\frac{5 a^3 b (a B+2 A b)}{3 x^3}-\frac{5 a^2 b^2 (a B+A b)}{x^2}+b^4 \log (x) (5 a B+A b)-\frac{5 a b^3 (2 a B+A b)}{x}+b^5 B x \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.163076, antiderivative size = 104, 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 \[ -\frac{a^5 A}{5 x^5}-\frac{a^4 (a B+5 A b)}{4 x^4}-\frac{5 a^3 b (a B+2 A b)}{3 x^3}-\frac{5 a^2 b^2 (a B+A b)}{x^2}+b^4 \log (x) (5 a B+A b)-\frac{5 a b^3 (2 a B+A b)}{x}+b^5 B x \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^5*(A + B*x))/x^6,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{5}}{5 x^{5}} - \frac{a^{4} \left (5 A b + B a\right )}{4 x^{4}} - \frac{5 a^{3} b \left (2 A b + B a\right )}{3 x^{3}} - \frac{5 a^{2} b^{2} \left (A b + B a\right )}{x^{2}} - \frac{5 a b^{3} \left (A b + 2 B a\right )}{x} + b^{5} \int B\, dx + b^{4} \left (A b + 5 B a\right ) \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**5*(B*x+A)/x**6,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0757304, size = 106, normalized size = 1.02 \[ -\frac{a^5 (4 A+5 B x)}{20 x^5}-\frac{5 a^4 b (3 A+4 B x)}{12 x^4}-\frac{5 a^3 b^2 (2 A+3 B x)}{3 x^3}-\frac{5 a^2 b^3 (A+2 B x)}{x^2}+b^4 \log (x) (5 a B+A b)-\frac{5 a A b^4}{x}+b^5 B x \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^5*(A + B*x))/x^6,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.012, size = 120, normalized size = 1.2 \[{b}^{5}Bx+A\ln \left ( x \right ){b}^{5}+5\,B\ln \left ( x \right ) a{b}^{4}-5\,{\frac{{a}^{2}{b}^{3}A}{{x}^{2}}}-5\,{\frac{{a}^{3}{b}^{2}B}{{x}^{2}}}-{\frac{A{a}^{5}}{5\,{x}^{5}}}-5\,{\frac{a{b}^{4}A}{x}}-10\,{\frac{{a}^{2}{b}^{3}B}{x}}-{\frac{10\,{a}^{3}{b}^{2}A}{3\,{x}^{3}}}-{\frac{5\,{a}^{4}bB}{3\,{x}^{3}}}-{\frac{5\,{a}^{4}bA}{4\,{x}^{4}}}-{\frac{{a}^{5}B}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^5*(B*x+A)/x^6,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34509, size = 155, normalized size = 1.49 \[ B b^{5} x +{\left (5 \, B a b^{4} + A b^{5}\right )} \log \left (x\right ) - \frac{12 \, A a^{5} + 300 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} + 300 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} + 100 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{2} + 15 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^5/x^6,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.201607, size = 163, normalized size = 1.57 \[ \frac{60 \, B b^{5} x^{6} + 60 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{5} \log \left (x\right ) - 12 \, A a^{5} - 300 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} - 300 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} - 100 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{2} - 15 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^5/x^6,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 9.49236, size = 117, normalized size = 1.12 \[ B b^{5} x + b^{4} \left (A b + 5 B a\right ) \log{\left (x \right )} - \frac{12 A a^{5} + x^{4} \left (300 A a b^{4} + 600 B a^{2} b^{3}\right ) + x^{3} \left (300 A a^{2} b^{3} + 300 B a^{3} b^{2}\right ) + x^{2} \left (200 A a^{3} b^{2} + 100 B a^{4} b\right ) + x \left (75 A a^{4} b + 15 B a^{5}\right )}{60 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**5*(B*x+A)/x**6,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.282032, size = 157, normalized size = 1.51 \[ B b^{5} x +{\left (5 \, B a b^{4} + A b^{5}\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{12 \, A a^{5} + 300 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} + 300 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} + 100 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{2} + 15 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^5/x^6,x, algorithm="giac")
[Out]