Optimal. Leaf size=117 \[ -\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{a^4 (a B+5 A b)}{19 x^{19}}-\frac{5 a^3 b (a B+2 A b)}{16 x^{16}}-\frac{a^5 A}{22 x^{22}}-\frac{a b^3 (2 a B+A b)}{2 x^{10}}-\frac{b^4 (5 a B+A b)}{7 x^7}-\frac{b^5 B}{4 x^4} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0649493, antiderivative size = 117, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {448} \[ -\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{a^4 (a B+5 A b)}{19 x^{19}}-\frac{5 a^3 b (a B+2 A b)}{16 x^{16}}-\frac{a^5 A}{22 x^{22}}-\frac{a b^3 (2 a B+A b)}{2 x^{10}}-\frac{b^4 (5 a B+A b)}{7 x^7}-\frac{b^5 B}{4 x^4} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{23}} \, dx &=\int \left (\frac{a^5 A}{x^{23}}+\frac{a^4 (5 A b+a B)}{x^{20}}+\frac{5 a^3 b (2 A b+a B)}{x^{17}}+\frac{10 a^2 b^2 (A b+a B)}{x^{14}}+\frac{5 a b^3 (A b+2 a B)}{x^{11}}+\frac{b^4 (A b+5 a B)}{x^8}+\frac{b^5 B}{x^5}\right ) \, dx\\ &=-\frac{a^5 A}{22 x^{22}}-\frac{a^4 (5 A b+a B)}{19 x^{19}}-\frac{5 a^3 b (2 A b+a B)}{16 x^{16}}-\frac{10 a^2 b^2 (A b+a B)}{13 x^{13}}-\frac{a b^3 (A b+2 a B)}{2 x^{10}}-\frac{b^4 (A b+5 a B)}{7 x^7}-\frac{b^5 B}{4 x^4}\\ \end{align*}
Mathematica [A] time = 0.0415233, size = 117, normalized size = 1. \[ -\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{a^4 (a B+5 A b)}{19 x^{19}}-\frac{5 a^3 b (a B+2 A b)}{16 x^{16}}-\frac{a^5 A}{22 x^{22}}-\frac{a b^3 (2 a B+A b)}{2 x^{10}}-\frac{b^4 (5 a B+A b)}{7 x^7}-\frac{b^5 B}{4 x^4} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 104, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{5}}{22\,{x}^{22}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{19\,{x}^{19}}}-{\frac{5\,{a}^{3}b \left ( 2\,Ab+Ba \right ) }{16\,{x}^{16}}}-{\frac{10\,{a}^{2}{b}^{2} \left ( Ab+Ba \right ) }{13\,{x}^{13}}}-{\frac{a{b}^{3} \left ( Ab+2\,Ba \right ) }{2\,{x}^{10}}}-{\frac{{b}^{4} \left ( Ab+5\,Ba \right ) }{7\,{x}^{7}}}-{\frac{B{b}^{5}}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.22549, size = 163, normalized size = 1.39 \begin{align*} -\frac{76076 \, B b^{5} x^{18} + 43472 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 152152 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 234080 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 95095 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 13832 \, A a^{5} + 16016 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{304304 \, x^{22}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.41678, size = 304, normalized size = 2.6 \begin{align*} -\frac{76076 \, B b^{5} x^{18} + 43472 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 152152 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 234080 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 95095 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 13832 \, A a^{5} + 16016 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{304304 \, x^{22}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.11635, size = 171, normalized size = 1.46 \begin{align*} -\frac{76076 \, B b^{5} x^{18} + 217360 \, B a b^{4} x^{15} + 43472 \, A b^{5} x^{15} + 304304 \, B a^{2} b^{3} x^{12} + 152152 \, A a b^{4} x^{12} + 234080 \, B a^{3} b^{2} x^{9} + 234080 \, A a^{2} b^{3} x^{9} + 95095 \, B a^{4} b x^{6} + 190190 \, A a^{3} b^{2} x^{6} + 16016 \, B a^{5} x^{3} + 80080 \, A a^{4} b x^{3} + 13832 \, A a^{5}}{304304 \, x^{22}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]