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Integrate the following and please simplify it.xtanx sec^2x dx

Integrate the following and please simplify it.xtanx sec^2x dx

Grade:11

1 Answers

Nandana
110 Points
6 years ago
hi !
  here,
Y =  ∫xtanxsec2 x dx
   take,
   U = x    dV =tanxsec2 x dx
  dU =1     V = ∫ tanx sec2 x dx
                    y = tanx
                   dy = sec2 x dx
                V = ∫ y dy = y2 /2 = tan2 x /2
    
    Y =  ½ x tan2 x – ½ ∫ tan2 x dx
       = ½ (xtan2 x – ∫(sec2 x -1)dx)
     Y  = ½ xtan2 x + x- tanx is the answer !
                 

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