Optimal. Leaf size=73 \[ \frac{x^{23}}{23}+\frac{11 x^{21}}{21}+\frac{55 x^{19}}{19}+\frac{165 x^{17}}{17}+22 x^{15}+\frac{462 x^{13}}{13}+42 x^{11}+\frac{110 x^9}{3}+\frac{165 x^7}{7}+11 x^5+\frac{11 x^3}{3}+x \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0217871, antiderivative size = 73, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {28, 194} \[ \frac{x^{23}}{23}+\frac{11 x^{21}}{21}+\frac{55 x^{19}}{19}+\frac{165 x^{17}}{17}+22 x^{15}+\frac{462 x^{13}}{13}+42 x^{11}+\frac{110 x^9}{3}+\frac{165 x^7}{7}+11 x^5+\frac{11 x^3}{3}+x \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 28
Rule 194
Rubi steps
\begin{align*} \int \left (1+x^2\right ) \left (1+2 x^2+x^4\right )^5 \, dx &=\int \left (1+x^2\right )^{11} \, dx\\ &=\int \left (1+11 x^2+55 x^4+165 x^6+330 x^8+462 x^{10}+462 x^{12}+330 x^{14}+165 x^{16}+55 x^{18}+11 x^{20}+x^{22}\right ) \, dx\\ &=x+\frac{11 x^3}{3}+11 x^5+\frac{165 x^7}{7}+\frac{110 x^9}{3}+42 x^{11}+\frac{462 x^{13}}{13}+22 x^{15}+\frac{165 x^{17}}{17}+\frac{55 x^{19}}{19}+\frac{11 x^{21}}{21}+\frac{x^{23}}{23}\\ \end{align*}
Mathematica [A] time = 0.0008704, size = 73, normalized size = 1. \[ \frac{x^{23}}{23}+\frac{11 x^{21}}{21}+\frac{55 x^{19}}{19}+\frac{165 x^{17}}{17}+22 x^{15}+\frac{462 x^{13}}{13}+42 x^{11}+\frac{110 x^9}{3}+\frac{165 x^7}{7}+11 x^5+\frac{11 x^3}{3}+x \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 58, normalized size = 0.8 \begin{align*} x+{\frac{11\,{x}^{3}}{3}}+11\,{x}^{5}+{\frac{165\,{x}^{7}}{7}}+{\frac{110\,{x}^{9}}{3}}+42\,{x}^{11}+{\frac{462\,{x}^{13}}{13}}+22\,{x}^{15}+{\frac{165\,{x}^{17}}{17}}+{\frac{55\,{x}^{19}}{19}}+{\frac{11\,{x}^{21}}{21}}+{\frac{{x}^{23}}{23}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.965563, size = 77, normalized size = 1.05 \begin{align*} \frac{1}{23} \, x^{23} + \frac{11}{21} \, x^{21} + \frac{55}{19} \, x^{19} + \frac{165}{17} \, x^{17} + 22 \, x^{15} + \frac{462}{13} \, x^{13} + 42 \, x^{11} + \frac{110}{3} \, x^{9} + \frac{165}{7} \, x^{7} + 11 \, x^{5} + \frac{11}{3} \, x^{3} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.52189, size = 180, normalized size = 2.47 \begin{align*} \frac{1}{23} x^{23} + \frac{11}{21} x^{21} + \frac{55}{19} x^{19} + \frac{165}{17} x^{17} + 22 x^{15} + \frac{462}{13} x^{13} + 42 x^{11} + \frac{110}{3} x^{9} + \frac{165}{7} x^{7} + 11 x^{5} + \frac{11}{3} x^{3} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.071701, size = 68, normalized size = 0.93 \begin{align*} \frac{x^{23}}{23} + \frac{11 x^{21}}{21} + \frac{55 x^{19}}{19} + \frac{165 x^{17}}{17} + 22 x^{15} + \frac{462 x^{13}}{13} + 42 x^{11} + \frac{110 x^{9}}{3} + \frac{165 x^{7}}{7} + 11 x^{5} + \frac{11 x^{3}}{3} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.11735, size = 77, normalized size = 1.05 \begin{align*} \frac{1}{23} \, x^{23} + \frac{11}{21} \, x^{21} + \frac{55}{19} \, x^{19} + \frac{165}{17} \, x^{17} + 22 \, x^{15} + \frac{462}{13} \, x^{13} + 42 \, x^{11} + \frac{110}{3} \, x^{9} + \frac{165}{7} \, x^{7} + 11 \, x^{5} + \frac{11}{3} \, x^{3} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]