Optimal. Leaf size=69 \[ \frac{5}{9} a^2 b^3 x^{18}+\frac{5}{8} a^3 b^2 x^{16}+\frac{5}{14} a^4 b x^{14}+\frac{a^5 x^{12}}{12}+\frac{1}{4} a b^4 x^{20}+\frac{b^5 x^{22}}{22} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.044137, 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} \[ \frac{5}{9} a^2 b^3 x^{18}+\frac{5}{8} a^3 b^2 x^{16}+\frac{5}{14} a^4 b x^{14}+\frac{a^5 x^{12}}{12}+\frac{1}{4} a b^4 x^{20}+\frac{b^5 x^{22}}{22} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^{11} \left (a+b x^2\right )^5 \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int x^5 (a+b x)^5 \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \left (a^5 x^5+5 a^4 b x^6+10 a^3 b^2 x^7+10 a^2 b^3 x^8+5 a b^4 x^9+b^5 x^{10}\right ) \, dx,x,x^2\right )\\ &=\frac{a^5 x^{12}}{12}+\frac{5}{14} a^4 b x^{14}+\frac{5}{8} a^3 b^2 x^{16}+\frac{5}{9} a^2 b^3 x^{18}+\frac{1}{4} a b^4 x^{20}+\frac{b^5 x^{22}}{22}\\ \end{align*}
Mathematica [A] time = 0.002101, size = 69, normalized size = 1. \[ \frac{5}{9} a^2 b^3 x^{18}+\frac{5}{8} a^3 b^2 x^{16}+\frac{5}{14} a^4 b x^{14}+\frac{a^5 x^{12}}{12}+\frac{1}{4} a b^4 x^{20}+\frac{b^5 x^{22}}{22} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 58, normalized size = 0.8 \begin{align*}{\frac{{a}^{5}{x}^{12}}{12}}+{\frac{5\,{a}^{4}b{x}^{14}}{14}}+{\frac{5\,{a}^{3}{b}^{2}{x}^{16}}{8}}+{\frac{5\,{a}^{2}{b}^{3}{x}^{18}}{9}}+{\frac{a{b}^{4}{x}^{20}}{4}}+{\frac{{b}^{5}{x}^{22}}{22}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.3269, size = 77, normalized size = 1.12 \begin{align*} \frac{1}{22} \, b^{5} x^{22} + \frac{1}{4} \, a b^{4} x^{20} + \frac{5}{9} \, a^{2} b^{3} x^{18} + \frac{5}{8} \, a^{3} b^{2} x^{16} + \frac{5}{14} \, a^{4} b x^{14} + \frac{1}{12} \, a^{5} x^{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.07144, size = 140, normalized size = 2.03 \begin{align*} \frac{1}{22} x^{22} b^{5} + \frac{1}{4} x^{20} b^{4} a + \frac{5}{9} x^{18} b^{3} a^{2} + \frac{5}{8} x^{16} b^{2} a^{3} + \frac{5}{14} x^{14} b a^{4} + \frac{1}{12} x^{12} a^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.070696, size = 65, normalized size = 0.94 \begin{align*} \frac{a^{5} x^{12}}{12} + \frac{5 a^{4} b x^{14}}{14} + \frac{5 a^{3} b^{2} x^{16}}{8} + \frac{5 a^{2} b^{3} x^{18}}{9} + \frac{a b^{4} x^{20}}{4} + \frac{b^{5} x^{22}}{22} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.51753, size = 77, normalized size = 1.12 \begin{align*} \frac{1}{22} \, b^{5} x^{22} + \frac{1}{4} \, a b^{4} x^{20} + \frac{5}{9} \, a^{2} b^{3} x^{18} + \frac{5}{8} \, a^{3} b^{2} x^{16} + \frac{5}{14} \, a^{4} b x^{14} + \frac{1}{12} \, a^{5} x^{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]