Optimal. Leaf size=83 \[ \frac{x^{25}}{25}+\frac{11 x^{23}}{23}+\frac{55 x^{21}}{21}+\frac{165 x^{19}}{19}+\frac{330 x^{17}}{17}+\frac{154 x^{15}}{5}+\frac{462 x^{13}}{13}+30 x^{11}+\frac{55 x^9}{3}+\frac{55 x^7}{7}+\frac{11 x^5}{5}+\frac{x^3}{3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0268132, antiderivative size = 83, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095, Rules used = {28, 270} \[ \frac{x^{25}}{25}+\frac{11 x^{23}}{23}+\frac{55 x^{21}}{21}+\frac{165 x^{19}}{19}+\frac{330 x^{17}}{17}+\frac{154 x^{15}}{5}+\frac{462 x^{13}}{13}+30 x^{11}+\frac{55 x^9}{3}+\frac{55 x^7}{7}+\frac{11 x^5}{5}+\frac{x^3}{3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 28
Rule 270
Rubi steps
\begin{align*} \int x^2 \left (1+x^2\right ) \left (1+2 x^2+x^4\right )^5 \, dx &=\int x^2 \left (1+x^2\right )^{11} \, dx\\ &=\int \left (x^2+11 x^4+55 x^6+165 x^8+330 x^{10}+462 x^{12}+462 x^{14}+330 x^{16}+165 x^{18}+55 x^{20}+11 x^{22}+x^{24}\right ) \, dx\\ &=\frac{x^3}{3}+\frac{11 x^5}{5}+\frac{55 x^7}{7}+\frac{55 x^9}{3}+30 x^{11}+\frac{462 x^{13}}{13}+\frac{154 x^{15}}{5}+\frac{330 x^{17}}{17}+\frac{165 x^{19}}{19}+\frac{55 x^{21}}{21}+\frac{11 x^{23}}{23}+\frac{x^{25}}{25}\\ \end{align*}
Mathematica [A] time = 0.0015298, size = 83, normalized size = 1. \[ \frac{x^{25}}{25}+\frac{11 x^{23}}{23}+\frac{55 x^{21}}{21}+\frac{165 x^{19}}{19}+\frac{330 x^{17}}{17}+\frac{154 x^{15}}{5}+\frac{462 x^{13}}{13}+30 x^{11}+\frac{55 x^9}{3}+\frac{55 x^7}{7}+\frac{11 x^5}{5}+\frac{x^3}{3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 62, normalized size = 0.8 \begin{align*}{\frac{{x}^{3}}{3}}+{\frac{11\,{x}^{5}}{5}}+{\frac{55\,{x}^{7}}{7}}+{\frac{55\,{x}^{9}}{3}}+30\,{x}^{11}+{\frac{462\,{x}^{13}}{13}}+{\frac{154\,{x}^{15}}{5}}+{\frac{330\,{x}^{17}}{17}}+{\frac{165\,{x}^{19}}{19}}+{\frac{55\,{x}^{21}}{21}}+{\frac{11\,{x}^{23}}{23}}+{\frac{{x}^{25}}{25}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.96931, size = 82, normalized size = 0.99 \begin{align*} \frac{1}{25} \, x^{25} + \frac{11}{23} \, x^{23} + \frac{55}{21} \, x^{21} + \frac{165}{19} \, x^{19} + \frac{330}{17} \, x^{17} + \frac{154}{5} \, x^{15} + \frac{462}{13} \, x^{13} + 30 \, x^{11} + \frac{55}{3} \, x^{9} + \frac{55}{7} \, x^{7} + \frac{11}{5} \, x^{5} + \frac{1}{3} \, x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.24423, size = 196, normalized size = 2.36 \begin{align*} \frac{1}{25} x^{25} + \frac{11}{23} x^{23} + \frac{55}{21} x^{21} + \frac{165}{19} x^{19} + \frac{330}{17} x^{17} + \frac{154}{5} x^{15} + \frac{462}{13} x^{13} + 30 x^{11} + \frac{55}{3} x^{9} + \frac{55}{7} x^{7} + \frac{11}{5} x^{5} + \frac{1}{3} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.068047, size = 75, normalized size = 0.9 \begin{align*} \frac{x^{25}}{25} + \frac{11 x^{23}}{23} + \frac{55 x^{21}}{21} + \frac{165 x^{19}}{19} + \frac{330 x^{17}}{17} + \frac{154 x^{15}}{5} + \frac{462 x^{13}}{13} + 30 x^{11} + \frac{55 x^{9}}{3} + \frac{55 x^{7}}{7} + \frac{11 x^{5}}{5} + \frac{x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13183, size = 82, normalized size = 0.99 \begin{align*} \frac{1}{25} \, x^{25} + \frac{11}{23} \, x^{23} + \frac{55}{21} \, x^{21} + \frac{165}{19} \, x^{19} + \frac{330}{17} \, x^{17} + \frac{154}{5} \, x^{15} + \frac{462}{13} \, x^{13} + 30 \, x^{11} + \frac{55}{3} \, x^{9} + \frac{55}{7} \, x^{7} + \frac{11}{5} \, x^{5} + \frac{1}{3} \, x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]