Optimal. Leaf size=73 \[ \frac {x^{21}}{21}+\frac {11 x^{19}}{19}+\frac {55 x^{17}}{17}+11 x^{15}+\frac {330 x^{13}}{13}+42 x^{11}+\frac {154 x^9}{3}+\frac {330 x^7}{7}+33 x^5+\frac {55 x^3}{3}+11 x-\frac {1}{x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 73, normalized size of antiderivative = 1.00, 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} \[ \frac {x^{21}}{21}+\frac {11 x^{19}}{19}+\frac {55 x^{17}}{17}+11 x^{15}+\frac {330 x^{13}}{13}+42 x^{11}+\frac {154 x^9}{3}+\frac {330 x^7}{7}+33 x^5+\frac {55 x^3}{3}+11 x-\frac {1}{x} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 28
Rule 270
Rubi steps
\begin {align*} \int \frac {\left (1+x^2\right ) \left (1+2 x^2+x^4\right )^5}{x^2} \, dx &=\int \frac {\left (1+x^2\right )^{11}}{x^2} \, dx\\ &=\int \left (11+\frac {1}{x^2}+55 x^2+165 x^4+330 x^6+462 x^8+462 x^{10}+330 x^{12}+165 x^{14}+55 x^{16}+11 x^{18}+x^{20}\right ) \, dx\\ &=-\frac {1}{x}+11 x+\frac {55 x^3}{3}+33 x^5+\frac {330 x^7}{7}+\frac {154 x^9}{3}+42 x^{11}+\frac {330 x^{13}}{13}+11 x^{15}+\frac {55 x^{17}}{17}+\frac {11 x^{19}}{19}+\frac {x^{21}}{21}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 73, normalized size = 1.00 \[ \frac {x^{21}}{21}+\frac {11 x^{19}}{19}+\frac {55 x^{17}}{17}+11 x^{15}+\frac {330 x^{13}}{13}+42 x^{11}+\frac {154 x^9}{3}+\frac {330 x^7}{7}+33 x^5+\frac {55 x^3}{3}+11 x-\frac {1}{x} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.64, size = 62, normalized size = 0.85 \[ \frac {4199 \, x^{22} + 51051 \, x^{20} + 285285 \, x^{18} + 969969 \, x^{16} + 2238390 \, x^{14} + 3703518 \, x^{12} + 4526522 \, x^{10} + 4157010 \, x^{8} + 2909907 \, x^{6} + 1616615 \, x^{4} + 969969 \, x^{2} - 88179}{88179 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.30, size = 59, normalized size = 0.81 \[ \frac {1}{21} \, x^{21} + \frac {11}{19} \, x^{19} + \frac {55}{17} \, x^{17} + 11 \, x^{15} + \frac {330}{13} \, x^{13} + 42 \, x^{11} + \frac {154}{3} \, x^{9} + \frac {330}{7} \, x^{7} + 33 \, x^{5} + \frac {55}{3} \, x^{3} + 11 \, x - \frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 60, normalized size = 0.82 \[ \frac {x^{21}}{21}+\frac {11 x^{19}}{19}+\frac {55 x^{17}}{17}+11 x^{15}+\frac {330 x^{13}}{13}+42 x^{11}+\frac {154 x^{9}}{3}+\frac {330 x^{7}}{7}+33 x^{5}+\frac {55 x^{3}}{3}+11 x -\frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.83, size = 59, normalized size = 0.81 \[ \frac {1}{21} \, x^{21} + \frac {11}{19} \, x^{19} + \frac {55}{17} \, x^{17} + 11 \, x^{15} + \frac {330}{13} \, x^{13} + 42 \, x^{11} + \frac {154}{3} \, x^{9} + \frac {330}{7} \, x^{7} + 33 \, x^{5} + \frac {55}{3} \, x^{3} + 11 \, x - \frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 59, normalized size = 0.81 \[ 11\,x-\frac {1}{x}+\frac {55\,x^3}{3}+33\,x^5+\frac {330\,x^7}{7}+\frac {154\,x^9}{3}+42\,x^{11}+\frac {330\,x^{13}}{13}+11\,x^{15}+\frac {55\,x^{17}}{17}+\frac {11\,x^{19}}{19}+\frac {x^{21}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 66, normalized size = 0.90 \[ \frac {x^{21}}{21} + \frac {11 x^{19}}{19} + \frac {55 x^{17}}{17} + 11 x^{15} + \frac {330 x^{13}}{13} + 42 x^{11} + \frac {154 x^{9}}{3} + \frac {330 x^{7}}{7} + 33 x^{5} + \frac {55 x^{3}}{3} + 11 x - \frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________