Optimal. Leaf size=122 \[ -\frac{a^3 \left (a+b x^2\right )^6 (A b-a B)}{12 b^5}+\frac{a^2 \left (a+b x^2\right )^7 (3 A b-4 a B)}{14 b^5}+\frac{\left (a+b x^2\right )^9 (A b-4 a B)}{18 b^5}-\frac{3 a \left (a+b x^2\right )^8 (A b-2 a B)}{16 b^5}+\frac{B \left (a+b x^2\right )^{10}}{20 b^5} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.650576, antiderivative size = 122, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\frac{a^3 \left (a+b x^2\right )^6 (A b-a B)}{12 b^5}+\frac{a^2 \left (a+b x^2\right )^7 (3 A b-4 a B)}{14 b^5}+\frac{\left (a+b x^2\right )^9 (A b-4 a B)}{18 b^5}-\frac{3 a \left (a+b x^2\right )^8 (A b-2 a B)}{16 b^5}+\frac{B \left (a+b x^2\right )^{10}}{20 b^5} \]
Antiderivative was successfully verified.
[In] Int[x^7*(a + b*x^2)^5*(A + B*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 37.547, size = 114, normalized size = 0.93 \[ \frac{A a^{5} x^{8}}{8} + \frac{B b^{5} x^{20}}{20} + \frac{a^{4} x^{10} \left (5 A b + B a\right )}{10} + \frac{5 a^{3} b x^{12} \left (2 A b + B a\right )}{12} + \frac{5 a^{2} b^{2} x^{14} \left (A b + B a\right )}{7} + \frac{5 a b^{3} x^{16} \left (A b + 2 B a\right )}{16} + \frac{b^{4} x^{18} \left (A b + 5 B a\right )}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7*(b*x**2+a)**5*(B*x**2+A),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0269963, size = 117, normalized size = 0.96 \[ \frac{1}{8} a^5 A x^8+\frac{1}{10} a^4 x^{10} (a B+5 A b)+\frac{5}{12} a^3 b x^{12} (a B+2 A b)+\frac{5}{7} a^2 b^2 x^{14} (a B+A b)+\frac{1}{18} b^4 x^{18} (5 a B+A b)+\frac{5}{16} a b^3 x^{16} (2 a B+A b)+\frac{1}{20} b^5 B x^{20} \]
Antiderivative was successfully verified.
[In] Integrate[x^7*(a + b*x^2)^5*(A + B*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 124, normalized size = 1. \[{\frac{{b}^{5}B{x}^{20}}{20}}+{\frac{ \left ({b}^{5}A+5\,a{b}^{4}B \right ){x}^{18}}{18}}+{\frac{ \left ( 5\,a{b}^{4}A+10\,{a}^{2}{b}^{3}B \right ){x}^{16}}{16}}+{\frac{ \left ( 10\,{a}^{2}{b}^{3}A+10\,{a}^{3}{b}^{2}B \right ){x}^{14}}{14}}+{\frac{ \left ( 10\,{a}^{3}{b}^{2}A+5\,{a}^{4}bB \right ){x}^{12}}{12}}+{\frac{ \left ( 5\,{a}^{4}bA+{a}^{5}B \right ){x}^{10}}{10}}+{\frac{{a}^{5}A{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7*(b*x^2+a)^5*(B*x^2+A),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34573, size = 161, normalized size = 1.32 \[ \frac{1}{20} \, B b^{5} x^{20} + \frac{1}{18} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{18} + \frac{5}{16} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{16} + \frac{5}{7} \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{14} + \frac{1}{8} \, A a^{5} x^{8} + \frac{5}{12} \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{12} + \frac{1}{10} \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5*x^7,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.216696, size = 1, normalized size = 0.01 \[ \frac{1}{20} x^{20} b^{5} B + \frac{5}{18} x^{18} b^{4} a B + \frac{1}{18} x^{18} b^{5} A + \frac{5}{8} x^{16} b^{3} a^{2} B + \frac{5}{16} x^{16} b^{4} a A + \frac{5}{7} x^{14} b^{2} a^{3} B + \frac{5}{7} x^{14} b^{3} a^{2} A + \frac{5}{12} x^{12} b a^{4} B + \frac{5}{6} x^{12} b^{2} a^{3} A + \frac{1}{10} x^{10} a^{5} B + \frac{1}{2} x^{10} b a^{4} A + \frac{1}{8} x^{8} a^{5} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5*x^7,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.174133, size = 136, normalized size = 1.11 \[ \frac{A a^{5} x^{8}}{8} + \frac{B b^{5} x^{20}}{20} + x^{18} \left (\frac{A b^{5}}{18} + \frac{5 B a b^{4}}{18}\right ) + x^{16} \left (\frac{5 A a b^{4}}{16} + \frac{5 B a^{2} b^{3}}{8}\right ) + x^{14} \left (\frac{5 A a^{2} b^{3}}{7} + \frac{5 B a^{3} b^{2}}{7}\right ) + x^{12} \left (\frac{5 A a^{3} b^{2}}{6} + \frac{5 B a^{4} b}{12}\right ) + x^{10} \left (\frac{A a^{4} b}{2} + \frac{B a^{5}}{10}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7*(b*x**2+a)**5*(B*x**2+A),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.225156, size = 169, normalized size = 1.39 \[ \frac{1}{20} \, B b^{5} x^{20} + \frac{5}{18} \, B a b^{4} x^{18} + \frac{1}{18} \, A b^{5} x^{18} + \frac{5}{8} \, B a^{2} b^{3} x^{16} + \frac{5}{16} \, A a b^{4} x^{16} + \frac{5}{7} \, B a^{3} b^{2} x^{14} + \frac{5}{7} \, A a^{2} b^{3} x^{14} + \frac{5}{12} \, B a^{4} b x^{12} + \frac{5}{6} \, A a^{3} b^{2} x^{12} + \frac{1}{10} \, B a^{5} x^{10} + \frac{1}{2} \, A a^{4} b x^{10} + \frac{1}{8} \, A a^{5} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5*x^7,x, algorithm="giac")
[Out]