Question

find the integration of this function​

Answer 1

Answer:

$\int \: ( {x}^{2} + 1)^{10} \\ = \int( {x}^{20} + 10 {x}^{18} + 45 {x}^{16} + 120 {x}^{14} + 210 {x}^{12} + 252 {x}^{10} + 210 {x}^{8} + 120 {x}^{6} + 45 {x}^{4} + 10 {x}^{2} + 1)dx \\ = \frac{ {x}^{21} }{21} + 10 \frac{ {x}^{19} }{19} + 45 \frac{ {x}^{17} }{17} + 120 \frac{ {x}^{15} }{15} + 210 \frac{ {x}^{13} }{13} + 252 \frac{ {x}^{11} }{11} + 210 \frac{ {x}^{9} }{9} + 120 \frac{ {x}^{7} }{7} + 45 \frac{ {x}^{5} }{5} + 10 \frac{ {x}^{3} }{3} + x + c$

Further simplifications required.