Optimal. Leaf size=69 \[ -\frac{5 a^3 b^2}{8 x^{16}}-\frac{5 a^2 b^3}{7 x^{14}}-\frac{5 a^4 b}{18 x^{18}}-\frac{a^5}{20 x^{20}}-\frac{5 a b^4}{12 x^{12}}-\frac{b^5}{10 x^{10}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0305198, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ -\frac{5 a^3 b^2}{8 x^{16}}-\frac{5 a^2 b^3}{7 x^{14}}-\frac{5 a^4 b}{18 x^{18}}-\frac{a^5}{20 x^{20}}-\frac{5 a b^4}{12 x^{12}}-\frac{b^5}{10 x^{10}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right )^5}{x^{21}} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{(a+b x)^5}{x^{11}} \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \left (\frac{a^5}{x^{11}}+\frac{5 a^4 b}{x^{10}}+\frac{10 a^3 b^2}{x^9}+\frac{10 a^2 b^3}{x^8}+\frac{5 a b^4}{x^7}+\frac{b^5}{x^6}\right ) \, dx,x,x^2\right )\\ &=-\frac{a^5}{20 x^{20}}-\frac{5 a^4 b}{18 x^{18}}-\frac{5 a^3 b^2}{8 x^{16}}-\frac{5 a^2 b^3}{7 x^{14}}-\frac{5 a b^4}{12 x^{12}}-\frac{b^5}{10 x^{10}}\\ \end{align*}
Mathematica [A] time = 0.0042634, size = 69, normalized size = 1. \[ -\frac{5 a^3 b^2}{8 x^{16}}-\frac{5 a^2 b^3}{7 x^{14}}-\frac{5 a^4 b}{18 x^{18}}-\frac{a^5}{20 x^{20}}-\frac{5 a b^4}{12 x^{12}}-\frac{b^5}{10 x^{10}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 58, normalized size = 0.8 \begin{align*} -{\frac{{a}^{5}}{20\,{x}^{20}}}-{\frac{5\,{a}^{4}b}{18\,{x}^{18}}}-{\frac{5\,{a}^{3}{b}^{2}}{8\,{x}^{16}}}-{\frac{5\,{a}^{2}{b}^{3}}{7\,{x}^{14}}}-{\frac{5\,a{b}^{4}}{12\,{x}^{12}}}-{\frac{{b}^{5}}{10\,{x}^{10}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 2.77342, size = 80, normalized size = 1.16 \begin{align*} -\frac{252 \, b^{5} x^{10} + 1050 \, a b^{4} x^{8} + 1800 \, a^{2} b^{3} x^{6} + 1575 \, a^{3} b^{2} x^{4} + 700 \, a^{4} b x^{2} + 126 \, a^{5}}{2520 \, x^{20}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.26214, size = 149, normalized size = 2.16 \begin{align*} -\frac{252 \, b^{5} x^{10} + 1050 \, a b^{4} x^{8} + 1800 \, a^{2} b^{3} x^{6} + 1575 \, a^{3} b^{2} x^{4} + 700 \, a^{4} b x^{2} + 126 \, a^{5}}{2520 \, x^{20}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.874056, size = 63, normalized size = 0.91 \begin{align*} - \frac{126 a^{5} + 700 a^{4} b x^{2} + 1575 a^{3} b^{2} x^{4} + 1800 a^{2} b^{3} x^{6} + 1050 a b^{4} x^{8} + 252 b^{5} x^{10}}{2520 x^{20}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.51817, size = 80, normalized size = 1.16 \begin{align*} -\frac{252 \, b^{5} x^{10} + 1050 \, a b^{4} x^{8} + 1800 \, a^{2} b^{3} x^{6} + 1575 \, a^{3} b^{2} x^{4} + 700 \, a^{4} b x^{2} + 126 \, a^{5}}{2520 \, x^{20}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]