integration of x^2×cos^2x
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∫x².cos²x.dx
use Tylor series of cos²x.
e.g cos²x = 1 - x² +x⁴/3 -2x⁶/45 + x⁸/315+........∞
use this ,
= ∫(x²-x⁴+x⁶/3 -2x⁸/45+.......∞)dx
= ∫x².dx -∫x⁴.dx+ 1/3∫x⁶.dx -2/45∫x⁸.dx +...
= x³/3 -x⁵/5 + x⁷/21 -2x⁹/405 +.......∞
use Tylor series of cos²x.
e.g cos²x = 1 - x² +x⁴/3 -2x⁶/45 + x⁸/315+........∞
use this ,
= ∫(x²-x⁴+x⁶/3 -2x⁸/45+.......∞)dx
= ∫x².dx -∫x⁴.dx+ 1/3∫x⁶.dx -2/45∫x⁸.dx +...
= x³/3 -x⁵/5 + x⁷/21 -2x⁹/405 +.......∞
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